Schulich School of Engineering, Department of Mechanical and Manufacturing Engineering
B.A. Classics, University of Calgary, 1993
B.S. Civil Engineering, University of Buenos Aires, 1967
Doctor of Philosophy Civil Engineering, Technion-Israel Institute Tech, 1972
M.S. Civil Engineering, Technion-Israel Institute Tech, 1970
|Course number||Course title||Semester|
|ENME 479 LEC 01 01||Mechanics Deformable¬†Solids II||Fall 2021|
|ENME 633 LEC 01 01||MathematicalTechnForEngineers||Winter 2022|
|LATI 205 LEC 01 01||The Latin of Science I||Fall 2021|
|LATI 207 LEC 01 01||The Latin of Science II||Winter 2022|
- Frank Spragins Technical Award, APEGA. 2020
- Tullio Levi-Civita award in Differential Geometry and Mechanics, International Research Center on Mathematics and Mechanics of Complex Systems. 2014
- CANCAM Medal , Canadian Congress of Applied Mechanics. 2009
- University Professorship in Rational Mechanics, University of Calgary. 2002
- Elected Fellow, American Academy of Mechanics. 2000
Professor, Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary
Dept of Mech and Manuf Engg, 2500 University Dr NW, Calgary, AB T2N1N4
Telephone: Work: 403-2205791
BSc (Cum Laude) University of Buenos Aires, 1967
MSc (Cum Laude) Technion, 1970
PhD Technion, 1972
BA (First Class Honours) University of Calgary, 1993
- Professor, Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary (1983-present)
- Adjunct Professor, Faculty of Humanities (Classics), U of C (2000-present)
- University Professor of Rational Mechanics, U of C (2002-2012)
- Adjunct Professor, Faculty of Kinesiology, U of C (1992-2012)
- Associate Professor, Mechanical Engineering, U of C (1979-1983)
- Assistant Professor, Mechanical Engineering, U of C (1976-1979)
- Research Associate, Civil Engineering, U of Alberta (1975-1976)
- Post-Doctoral Fellow, Civil Engineering, U of Alberta (1974-1975)
- Lecturer, Technion, Israel Institute of Technology (1972-1973)
- Instructor, Technion, Israel Institute of Technology (1969-1972)
- Ben-Gurion University of the Negev (June-July, 2019)
- Ben-Gurion University of the Negev (July-August, 2012)
- Polytechnic University of Valencia (September-December, 2011)
- Oxford Centre for Collaborative Applied Mathematics (November, 2010)
- Université Pierre et Marie Curie, Paris VI (May, 2008)
- Università di Roma II, Tor Vergata (January-June, 2005)
- Consejo Superior de Investigación Científica, Madrid (January- June,1999)
- University of Pisa (June 1-30, 1998)
- Université Pierre et Marie Curie, Paris VI, 6 weeks, 1997.
- Consejo Superior de Investigación Científica, Madrid (January-June,1994)
- Universidad Nacional de la Plata, Argentina (January- April, 1990)
- Université Pierre et Marie Curie, Paris VI (September - December, 1989)
- Ben Gurion University of the Negev (January - June, 1983)
- Interim Head, Department of Mechanical and Manufacturing Engineering, University of Calgary, January – December, 2014
- Associate Head (Graduate Studies), Department of Mechanical Engineering, University of Calgary, July 1997 – June 1999
- Associate Head (Graduate Studies), Department of Mechanical Engineering, University of Calgary, July 1996 – June 1997
- Associate Dean (Research), Faculty of Engineering, University of Calgary, July 1996 - June 1997
2020 Frank Spragins Technical Award, APEGA Summit Award
2017 Special Issue of the journal Mathematics and Mechanics of Solids (“The issue is dedicated to Professor Marcelo Epstein (University of Calgary) who has been one of the most significant contributors to the subject in the last four decades.”)
2015 Honoree of the 53rd meeting of the Society for Natural Philosophy, Calgary, August, 2015.
2014 Tullio Levi-Civita award in Differential Geometry and Mechanics (“For his innovative way of linking geometrical concepts to mechanical and biological phenomena. He can be considered as a founding father in continuum mechanics and its applications, including geometrical mechanics of defects, theory of inhomogeneities, configurational mechanics, and mechanics of muscles.”). Awarded by the International Research Center on Mathematics and Mechanics of Complex Systems, at the 17th U.S. National Congress on Theoretical and Applied Mechanics, held in Lansing, Michigan, in June 2014,
2013 Included in the section of selected biographies in the major historical work by G.A. Maugin (Continuum Mechanics through the Twentieth Century, Springer-Verlag). One of only two Canadians on this list.
2009 CANCAM Medal (“For his outstanding contributions to the area of Applied Mechanics”). The award ceremony took place in Halifax, Nova Scotia, during the 21st Canadian Congress of Applied Mechanics, June 2009.
2005 Research Excellence Award, Department of Mechanical and Manufacturing Engineering, University of Calgary.
2002 University Professorship in Rational Mechanics, University of Calgary.
2000 Elected Fellow of the American Academy of Mechanics (AAM)
Courses created at U of C
- ENME 547: The finite element method in Engineering. This course was established in 1985 to address the then growing demand for mechanical engineers with a solid background in the finite element method and its applications. The course has been taught ever since as a 4-th year undergraduate technical elective, and occasionally as a graduate course.
- ENME 653: Continuum Mechanics. Established ca. 1990, this graduate course has attracted students from several departments, including Mechanical, Civil, Chemical and Petroleum Engineering, Kinesiology, and Geophysics. It is still being taught to this day.
- LATI 205 and LATI 207: The Latin of Science. Established in the Fall of 1999, these two popular courses, that draw undergraduate students from Engineering, Sciences and the Humanities, are being successfully taught and keep attracting students from varied backgrounds.
Courses taught over the years (listed only those taught more than 10 times)
- ENGG 202: Engineering Statics
- ENGG 317: Mechanics of Solids
- ENGG 349: Dynamics
- ENME473: Fundamentals of Kinematics and Dynamics of Machines
- ENME470: Mechanics of Deformable Solids II
- ENME 547: Finite Element Method
- ENME 633: Mathematical Techniques for Engineers
- ENME 653: Advanced Continuum Mechanics
- LATI 205: The Latin of Science I
- LATI 207: The Latin of Science II
- The `Galileo Program’. Proposed first in 1992, this initiative advocated the fully-fledged development of an Honours Engineering Science Progra, A pilot project was launched which functioned for the next 5 years. In collaboration with Dr. A. Jeje (from Chemical and Petroleum Engineering), we offered high-level versions of courses in Solid and Fluid Mechanics for cohorts of about 20 students with outstanding academic credentials The initiative was eventually abandoned for lack of funding.
- A 1994 proposal on a degree in ‘Humanistic Engineering’, based on the concept of Engineering as a liberal discipline, led to presentations at U of C and the University of Victoria, and also to a publication in a national journal. It was never implemented in practice, but it begat a short-lived course in Reading of Original Scientific Texts and, eventually, the courses on the Latin of Science, still being taught after more than 20 years.
Graduate and post-graduate supervision
- Supervised 25 graduate students who completed their MSc or PhD theses.
- Hosted 12 foreign graduate students who spent various periods of time under my supervision as part of their graduate programs.
- Supervised 9 Research Associates and Post-Doctoral Fellows.
NOTE: Each entry is followed by a short description of the content and impact of the work
- Material Geometry: Groupoids in Continuum Mechanics, World Scientific, 2021. Co-authored with Manuel de León and Victor Jimenez.
This research monograph is designed to fill a gap in the applied mathematics literature. The theory of groupoids is less than a century old. In recent years, it has been found to unify the structure of many physical theories with unparalleled power and elegance. In the field of Solid Mechanics, in joint work over the last 20 years with Manuel de León (Madrid), we have laid the foundations of the general theory of continuously distributed defects in materials in terms of groupoids. This book addresses the need to provide a presentation of the theory and its applications amenable to applied researchers.
- GeometricContinuum Mechanics, Springer Nature, Birkhäuser. 2020. Co-edited with Reuven Segev.
From the publisher: “Explores the mathematical foundations of continuum mechanics with a particular focus on geometric methods. Introduces applications of global analysis, algebraic topology, algebroids, groupoids, and geometric measure theory to continuum mechanics. Includes chapters written by authors who are experts in their respective areas, providing important insights from recent research.”
- The Latin of Science, Bolchazy-Carducci Publishers, Bolchazy-Carducci, 2019. Co-authored with Ruth Spivak.
Two courses on The Latin of Science have been established since 1995 at the University of Calgary. These courses can be considered unique in nature, since they are addressed to non-Classics majors while leading to a thorough ability to read scientific texts, written during a period of more than 20 centuries, in their original Latin version. In this book, now under production, we provide profusely annotated texts covering diverse scientific areas (such as Architecture, Astronomy, Medicine, Economics, Optics, and Philosophy of Science). An unusual feature of the book is that it provides the reader with facsimiles of manuscripts or first editions, intended to enhance the feeling of authenticity, much as when playing music in original period instruments. The book contains a complete grammar of the Latin language written in the spirit of science students, who look for patterns of similarity rather than minor differences, as is common in books written for Classics majors, who are driven to read classical Latin poetry or oratory.
- Partial Differential Equations, Springer, 2017.
Having taught for several years a graduate course (ENME 633) in PDEs and having developed a full set of notes and exercises relevant to Engineering applications, I decided to organize the material and propose it as a book for the Springer series Mathematical Techniques for Engineers. Although many other books exist, it appears that this book has been able to find a good balance between theory and applications, staying away from excesses in either direction. The target audience comprises primarily graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry. The total number of chapter downloads from the Springer platform has been more than 13,600 since its recent publication.
- Differential Geometry, Springer, 2014.
Subtitled “Basic Notions and Physical Examples”, this book offers a concise introduction to the foundational ideas of modern Differential Geometry, with a view to its applications to Physics and Solid Mechanics. The book is the outgrowth of a mini-course delivered at the International Centre for Mathematical Sciences (ICMS) for a workshop on Differential Geometry and Continuum Mechanics held in Edinburgh in June 2013. The MAA Reviews stated that “this book is a gold mine of aesthetically pleasing mathematical ideas, the presentation of which is highly inspirational.” To date, the book or parts thereof has been downloaded from the Springer platform more than 13,500 times, apart from ordinary sales.
- The Elements of Continuum Biomechanics, Wiley, 2012.
This book is intended to serve as a high-level introduction for researchers applying the techniques of Continuum Mechanics to modeling biological tissues. The book is sprinkled with `case studies’, each of which presents a non-trivial application of the theory, including such non-standard topics as the use of mixture theory involving chemical reactions. Although not originally intended to display original research, the book has been cited 20 times in peer-reviewed journals.
- The Geometrical Language of Continuum Mechanics, Cambridge University Press, 2010.
This work presents a view of the discipline that summarizes the point of view propounded over a period of three decades with my collaborators. As such, it can be regarded as a labour of love, enhanced by the careful and elegant format provided by Cambridge University Press. The book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics. The abstract notions of differential geometry are illuminated by practical and intuitively meaningful engineering applications. An indication of the influence of this book in the Applied Mechanics community is that it has been cited over 100 times in articles published in peer-reviewed journals.
- Material Inhomogeneities and their evolution, Springer, 2007. Co-authored with M. Elzanowski.
This specialized monograph presents an original unified treatment of inhomogeneity theory using the tools of modern differential geometry.
Inhomogeneity theory is of importance for the description of a variety of material phenomena, including continuous distributions of dislocations, fracture mechanics, plasticity, biological remodelling and growth and, more generally, all processes that entail changes in the material body driven by forces known in literature as material or configurational. Chapters of this monograph have been downloaded from the Springer platform 5,100 times.
- Theoretical Models of Skeletal Muscle, Wiley, 1998. Co-authored with W. Herzog.
Written in collaboration with Walter Herzog, presently the Director of our prestigious Human Performance Laboratory, this book presents a thorough examination of the basic physiology and mechanics of skeletal muscle. This book is unique in the field and has had an unparalleled impact on the Biomechanics community, as demonstrated by over 220 citations. It is currently out of print.
Articles in peer-reviewed journals
(Source: Google Scholar)
NOTE: Indented entries contain a short description of the paper
Epstein M (2021), Material Geometry of Binary Composites, Symmetry 13/5, 892
Defaz R I, Epstein M and Federico S (2021), Analysis of Solitary Waves in Fluid-filled Thin-walled Electroactive Tubes, Mechanics Research Communications 13, 103654
Defaz R I, Epstein M and Federico S (2021), The Domain of Existence of Solitary Waves in Fluid-filled Thin Elastic Tubes, Mathematics and Mechanics of Solids, 1081286520984819
Atieh A M and Epstein M (2021), The Method of Spatio-temporal Variable Diffusivity (STVD) for Coupled Diffusive Processes, Mechanics Research Communications 111, 103649
Atieh A M and Epstein M (2020), The Role of Nanomaterials in Diffusive Processes: The case of Transient Liquid Phase (TLP) Bonding, Materials Today Communications 25, 101481
Javadi M, Epstein M and Asghari M (2020), Micromorphic Balance Equations in Mass Transport and Mass Production, International Journal of Engineering Science 153, 103312
Epstein M (2020), Reflections on the Structural and Constitutive Approaches to the Theory of Defects, Mechanics Research Communications 107, 103548
Jiménez V M, de Leόn M and Epstein M (2020), Material Distributions, Mathematics and Mechanics of Solids 25/7, 1450-1458
Epstein M (2020), Hilbert bundles as quantum-classical continua, Mathematics and Mechanics of Solids 25/6, 1312-1317
Epstein M and Smelser R (2020), An Aprreciation and Discussion of Paul Germain’s “The Method of Virtual Power in the Mechanics of Continuous Media, I: Second-Gradient Theory”, Mathematics and Mechanics of Complex System 8/2, 191-199
Epstein M and Segev R (2020), Regular and Singular Dislocations, in Geometric Continuum Mechanics, Birkhäuser, 223-266
Epstein M, Kupferman R and Maor C (2020), Limits of Distributed Dislocations in Geometric and Constitutive Paradigms, in Geometric Continuum Mechanics, Birkhäuser, 349-380
Javadi M, Epstein M and Asghari M (2020), Thermomechanics of Material Growth and Remodeling in Uniform Bodies Based on the Micromorphic Theory, Journal of the Mechanics and Physics of Solids 138, 103904
Jiménez V M, de Leόn M and Epstein M (2020), On the Homogeneity of Non-uniform Material Bodies, in Geometric Continuum Mechanics, Birkhäuser, 381-420
Javadi M and Epstein M (2019), Invariance in Growth and Mass Transport, Mathematics and Mechanics of Solids 24/6, 1707-1713
Epstein M and de León M (2019), Material groupoids and algebroids, Mathematics and Mechanics of Solids 24/3, 796-806
Hamedzadeh A, Grillo A, Epstein M and Federico S (2019), Remodelling of Biological Tissues with Fibre Recruitment and Reorientation in the Light of the Theory of Material Uniformity, Mechanics Research Communications 96, 56–61.
Epstein M, Jiménez V M and de León M (2019), Material Geometry, Journal of Elasticity 135/1-2, 237-260
Javadi M and Epstein M (2019), Invariance in growth and mass transport, Mathematics and Mechanics of Solids 24/6, 1707-1713. DOI: 1081286518787845
Alhasadi M F, Epstein M and Federico S (2019), Eshelby force and power for uniform bodies, Acta Mechanica 230/5, 1663-1684.
Epstein M and Segev R (2019), Vlasov’s Beam Paradigm and Multivector Grassmann Statics, Mathematics and Mechanics of Solids 24/10, 3167-3179
- Epstein M (2018), Affine n-dimensional Statics, affine screws and Grassmann algebra, Mechanics Research Communications 94, 74-79. Comments: The theory of screws is generalized to yield a formulation of Statics in higher-dimensional spaces in the absence of any distinguished metric structure. This level of generality necessitates the use of the tools of the exterior algebra of multi-vectors. The minimal structure retained serves to bring into relief the essential difference between screws and counter-screws as well as a weak version of the notion of rigid-body velocity field. An essential feature of the theory is the introduction of higher-order forces and displacements, whose relevance in the context of structured media can be determined in specific potential applications.
- Epstein M (2018), The dual approach to smooth defects, in Generalized Models and Non-Classical Approaches in Complex Materials 1 (Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, Th. (Eds.)), 287-300. Comments: Within the theory of continuous distributions of defects in materials, this paper advocates a point of view based on the geometry of differential forms. Applications to smectic liquid crystals and to multi-walled nanotube composites serve to show how this dual mathematical approach fits perfectly with the intended physical reality. Moreover, the weak formulation of the theory in terms of de Rham currents delivers the description of discrete isolated dislocations as a generalization of the smooth theory.
Jiménez V M, de León M and, Epstein M (2018), Characteristic distribution: An application to material bodies, Journal of Geometry and Physics 127, 19-31
Jiménez V M, de León M and, Epstein M (2018), Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media, International Journal of Geometric Methods in Modern Physics 15/08, 1830003.
Epstein M (2018), Laminated uniformity and homogeneity, Mechanics Research Communications 93, 66-69.
Jiménez V M, de León M and Epstein M (in press), Material distributions, Mathematics and Mechanics of Solids, DOI: 1081286517736922
- Epstein M (2016), Modeling continuous distributions of dislocations in multi-walled nanotube composites, ZAMP (Zeitschrift für angewandte Mathematik und Physik) 67/6, 141-156. Comments: A modeling paradigm for continuous distributions of defects in multi-walled nanotube composites is proposed based on the theory of differential forms. A necessary and sufficient condition for a defect-free composite is derived and, concomitantly, a measure of defect density is proposed. Mathematically, this condition ensures the consistency of an over-determined system of partial differential equations. Physically, the condition expresses the fact that each multi-layered nanotube can find mutually coherent nanotubes in its neighborhood. Several examples of defect-free arrangements are presented and discussed.
Epstein M and de León M (2016), Unified geometric formulation of material uniformity and evolution, Mathematics and Mechanics of Complex Systems 4/1, 17-29.
- Epstein M (2015), Mathematical characterization and identification of remodeling, growth, aging and morphogenesis, Journal of the Mechanics and Physics of Solids 84, 72-84. Comments: In this paper, the various phenomena occurring in the evolution and growth of biological tissues are classified according to a rigorous mathematical criterion. More importantly, it is shown that, for certain cases (depending on the underlying material symmetry, such as isotropy and orthotropy), a sharp separation between these phenomena can be determined unequivocally. The importance of this fact is that experimentally measured properties can be attributed to each of these phenomena separately. Moreover, the generation of patterns (morphogenesis) can be described in terms of a symmetry braking that may be produced by purely mechanical (rather than chemical) causes.
Epstein M and Roychowdhury A (2015), Embedded homogeneity of beams in the nonlinear domain, International Journal of Solids and Structures, 58, 201-206.
Boraey MA, Guaily A and Epstein M (2015), A hybrid model for biofilm growth on a deformable substratum, The Canadian journal of Chemical Engineering, 93/5, 789-797.
- Epstein M and Segev R (2014), Geometric aspects of singular dislocations, Mathematics and Mechanics of Solids, 19/4, 337-349. Comments: The passage from the smooth theory of distributed defects (shown to be describable in terms of differential forms) to the singular theory of isolated defects is achieved by the use of the theory of de Rham currents. A de Rham current can be regarded as a kind “Dirac delta” version of a differential form. Frank’s rules for dislocations and disclinations are shown to be straightforward consequences of the fact that the boundary of a boundary necessarily vanishes.
Epstein M and Segev R (2014), Geometric theory of smooth and singular defects, International Journal of Nonlinear mechanics, 66, 105-110.
Epstein M and Roychowdhury A (2014), On the notion of embedded homogeneity of thin structures, Mathematics and Mechanics of Solids, web preprint: 1081286514535127
Moo E K, Amrein M, Epstein M, Duvall M, Abu Osman NA, Pingguan-Murphy B and Herzog W (2014), Strain-rate dependent membrane reservoir, key to chondrocyte death by impact, Biophysical Journal, 106 (2), 451a.
Ju Y, Zheng J, Epstein M, Sudak L, Wang J, Zhao X (2014), 3D numerical reconstruction of well-connected porous structure of rock using fractal algorithms, Computer Methods in Applied Mechanics and Engineering, 279/1, 212-226.
Lazaro M, Perez Aparicio J L and Epstein M (2013), A viscous approach based on oscillatory eigensolutions for viscoelastically damped vibrating systems, Mechanical Systems and Signal Processing 40/2, 767-782.
Moo E K, Amrein M, Epstein M, Duvall M, Abu Osman N A, Pingguan-Murphy B and Herzog W (2013), The properties of chondrocyte membrane reservoirs and their role in impact-induced cell death, Biophysical Journal 105/7, 1590-1600.
Guaily A G and Epstein M (2013), Boundary conditions for hyperbolic systems of partial differential equations, Journal of Advanced Research 4/4, 321-329.
Epstein M and Goriely A (2012), Self-diffusion in remodelling and growth, ZAMP 63, 339-355.
Epstein M, Peter D and Slawinski M A (2012), Combining Ray-Tracing Techniques and Finite-Element Modelling in Deformable Media, The Quarterly Journal of Mechanics and Applied Mathematics 65, 87-112.
Lázaro M, Pérez-Aparicio J L and Epstein M (2012), Computation of eigenvalues in proportionally damped viscoelastic structures based on the fixed-point iteration, Applied Mathematics and Computation 219/8, 3511-3529.
Epstein M (2011), Media with semiholonomic internal structure, Journal of Mechanics of Materials and Structures 6/1-4, 169-179.
Guaily A, Cheluget E, Lee K and Epstein M (2011), A New Hyperbolic Model and an Experimental Study for the Flow of Polymer Melts in Multi-Pass Rheometer, Computers and Fluids 44/1, 258-266.
Bongue-Boma M, Epstein M and Federico S (2011), A Continuum Model of Negatively Charged Rods Finely Dispersed in a Positively Charged Fluid, Mechanics Research Communications 38/8, 574-578.
Nadler B and Epstein M (2011), Slip-plane plasticity using the theory of material evolution. Math. Mech. of Solids 16, 381-392.
Epstein M (2010), Kinetics of Boundary Growth, Mechanics Research Communications 37, 453-457.
Epstein M and Maugin G A (2010), Remarks on the universality of the Eshelby stress, Mathematics and Mechanics of Solids 15/1, 137-143.
Boraey M and Epstein M (2010), Lattice Boltzmann Modeling of Viscous Elementary Flows, Adv. Appl. Math. Mech. 2/4, 467-482.
Epstein M (2010), Semiholonomic Cosserat Media , in Advances in Mechanics and Mathematics, Vol. 21: Mechanics of Generalized Continua, One hundred years after the Cosserats (G.A. Maugin and A.V. Metrikine, editors), Springer, 15-24.
Johnston C and Epstein M (2010), The validity of the long-wave approximation for solitary waves in fluid-filled elastic tubes, Zeitschrift für angewandte Mathematik und Physik (ZAMP) 61/5, 1133-1143.
Guaily A and Epstein M (2010), A hybrid finite element/finite difference algorithm for compressible/incompressible viscoelastic liquid, The Canadian Journal of Chemical Engineering 88/6, 959-974.
Guaily A and Epstein M (2010) A unified hyperbolic model for viscoelastic liquids, Mechanics Research Communications 37, 158–163.
Epstein M (2009), The split between remodeling and aging, International Journal of Non-Linear Mechanics 44, 604-609.
Adeeb S and Epstein M (2009), Fractal Elements, Journal of Mechanics of Materials and Structures, 4/5, 781-797.
Epstein M and Adeeb S (2008), The stiffness of self-similar fractals, International Journal of Solids and Structures 45, 3238-3254.
Epstein M (2008), The projected first-grade material of a structured medium, International Journal of Nonlinear Mechanics 43, 341-344.
Epstein M and Sniatycki J (2008), The Koch curve as a smooth manifold, Chaos, Solitons and Fractals 38,. 334-338.
Lemos R R, Epstein M and Herzog W (2008), Modeling of skeletal muscle: the influence of tendon and aponeuroses compliance on the force-length relationship, Medical and Biological Engineering and Computing, 46/1, 23-32.
Campos C M, Epstein M and de León M (2008), Functionally graded media, International Journal of Geometric Methods in Modern Physics 5/3, 431-455.
Epstein M (2007), Configurational balance and entropy sinks, International Journal of Fracture 147, 35-43.
Rouhi GR, Epstein M, Sudak L and Herzog W (2007), Modeling bone resorption process using mixture theory with chemical reactions: theoretical considerations, Journal of Mechanics of Materials and Structures 2/6, 1141-1155
- Epstein M, Burton D and Tucker R (2006), Relativistic anelasticity, Classical and Quantum Gravity 23, 3545-3571. Comments: Teaming up with the English physicist Robin Tucker at the University of Lancaster, we considered the general relativistic version of a deformable anelastic body. One of the intriguing consequences of the analysis is that the spatial (uniformity) and temporal (evolution) of the classical formulation can no longer be split, but are observer-dependent.
- Epstein M and Sniatycki J (2006), Fractal Mechanics, Physica D 220, 54-68. Comments: The geometrical theory of fractals, popularized among others by Benoit Mandelbrott, is well established. Nevertheless, if a material body can be considered to possess a fractal structure, how are we to express its elastic properties and mechanical response? In this article, we propose a formulation based on the geometrical theory of differential spaces, first introduced by Sikorski. A differential space is not necessarily a “continuum” and thus it lends itself to the possibility of describing more general material bodies.
Rouhi GR, Epstein M., Herzog W, Sudak, L (2006), Free Surface Density & Microdamage in the bone Remodeling Equation: Theoretical Considerations, International Journal of Engineering Science 44/7, 456-469
Epstein M, Wong M, Herzog W (2006), Should tendon and aponeurosis be considered in series?, Journal of Biomechanics 39/11), 2020-2025
Epstein M and Defaz R I (2005), The Pseudo-Rigid Rolling Coin, ASME Journal of Applied Mechanics 72, 695-704.
Villanueva R and Epstein M (2005), Vibrations of Euler’s Disk, Physical Review E 71, 066609:1-7.
Han, S-K, Federico S, Epstein M and Herzog W (2005), An articular cartilage contact model based on real surface geometry, Journal of Biomechanics 38/1, 179-184
Epstein M and Sniatycki J (2005), Nonlocal Inhomogeneity and Eshelby Entities, Phil Mag 85/33-35, 3939-3955
Rouhi R, Herzog W, Sudak L, Firoozbakhsh K and Epstein M (2005), Free surface density instead of volume fraction in the bone remodelling equation: theoretical considerations, FORMA 19/3, 165-182
Epstein M (2005), Self-Driven Continuous Dislocations and Growth, in Mechanics of Material Forces (P. Steinmann and G. Maugin, eds., Springer), Advances in Mechanics and Mathematics 11, 129-139
Bucataru I and Epstein M (2004), Geometrical theory of dislocation in bodies with microstructure, J of Geometry and Physics 52/1, 57-73
Lemos R R, Epstein M, Herzog W and Wyvill B (2004), A framework for structured modelling of skeletal muscle, Computer Methods in Biomechanics and Biomedical Engineering 7/6, 305-317
Epstein M (2003), Differential Equation for the Amplitude of Wrinkles, AIAA Journal. 41, 327-329.
- Epstein M. and Herzog W (2003), Aspects of Skeletal Muscle Modeling, Phil. Trans. R. Soc. London B 358, 1445-1452. Comments: Working together with Walter Herzog, in this article we explore the scientific and philosophical underpinnings of the mechanical modeling of biological systems.
Epstein M and Bucataru I (2003), Continuous Distributions of Dislocations in Bodies with Microstructure, Journal of Elasticity 70/1, 237-254
Epstein M and Elzanowski M (2003), A Model of the Evolution of a Two-dimensional Defective Structure, Journal of Elasticity, 70/1, 255-265
Epstein M (2002), From Saturated Elasticity to Finite Plasticity and Growth, Mathematics and Mechanics of Solids 7, 255-283.
Epstein M (2002), The Eshelby Tensor and the Theory of Continuous Distributions of Inhomogeneities, Mechanics Research Communications 29, 501-506.
- Epstein M and Johnston C R (2001), On the Exact Speed and Amplitude of Solitary Waves in Fluid-Filled Elastic Tubes, Proc. Royal Society London A457, 1195-1214. Comments: The standard perturbation solution of the problem of solitary waves in arteries is shown to be in error. Instead, we show how to solve it with any specified degree of accuracy. The proposed solution is exact, except for a step involving the finding of the root of an algebraic equation.
Epstein M and de León M (2001), Continuous distributions of inhomogeneities in liquid-crystal-like bodies, Proc. Royal Society London A457, 2507-2520.
Spivak M and Epstein M (2001), On Newton's Psychosis, The American Journal of Psychiatry 158, 821-822.
Epstein M. and Forcinito M A (2001), Anisotropic Membrane Wrinkling: Theory and Analysis, International Journal of Solids and Structures 38, 5253-5272.
Babaei R, Epstein M and Lukasiewicz S (2001), Delamination Analysis of Layered Shells, Journal of Composite Materials, 35/21, 1891-1923
- Johnston C R and Epstein M (2000), On the Exact Amplitude, Speed and Shape of Ion-Acoustic Waves, Physics of Plasmas 7, 906-910. Comments: This article has a curious history, since the area of Plasma Physics is neither my specialty nor that of my former PhD student Clifton Johnston (now an NSERC chair in Nova Scotia). The article, however, aroused significant interest in the Plasma community since it succeeded in obtaining an exact solution for a problem of propagation of nonlinear ion-acoustic solitary waves in cold collisionless plasma. Most importantly, we showed that the error committed by the use of standard perturbation techniques is very significant and can lead to severe underestimation of the amplitude of the wave.
- Epstein M and Maugin G A (2000), Thermomechanics of Volumetric Growth in Uniform Bodies, Int. J. of Plasticity 16, 951-978. Comments: This paper has become a standard reference in the area of volumetric growth. It presents the rigorous mechanical and thermodynamical foundations for the formulation of theories of biological growth within the context of continuum mechanics.
Epstein M and de León, M (2000), Homogeneity Without Uniformity: Toward a Mathematical Theory of Functionally Graded Materials, Int Journal of Solids and Structures, 37, 7577-7591
Wu J Z, Herzog W and Epstein M (2000), Joint Contact Mechanics in the Early Stages of Osteoarthritis, Medical Engineering and Physics 22, 1-12.
Epstein M and Maugin G A (2000), Material Evolution in Plasticity and Growth, in Continuum Thermomechanics, Volume in Honour of Professor Paul Germain, Kluwer Academic Publishers
Epstein M and Slawinsk, M A (2000), Rays and Ray Parameters in Inhomogeneous Isotropic Media, CSEG Journal 35/12, 7-19
Epstein M and Slawinski M A (2000), On Raytracing in Constant-Velocity-Gradient Media: Geometrical Approach, CSEG Journal 35/12, 1-6
Epstein M (2000), On the Extended Notion of Material Homogeneity, Technische Mechanik 20/2, 169-172
Lemos R, Epstein M, Herzog W and Wyvill B (2000), Three-dimensional Geometric Model of Skeletal Muscle, in Skeletal Muscle Mechanics (W. Herzog ed., Wiley), 179-205
Epstein M (2000), Are continuous distributions of inhomogeneities in liquid crystals possible?, Rendiconti del Seminario Matematico dell'Universita e del Politecnico di Torino 58/1, 93-98
- Epstein M (1999), Toward a Complete Second Order Evolution Law, Mathematics & Mechanics of Solids 4, 251-266. Comments: Second-grade materials, whose internal forces can be said to have a longer range than ordinary first-grade materials, require rather sophisticated mathematical tools, particularly in what pertains to the description of distributed material defects. This article presents the correct framework for the formulation of laws of evolution of these defects.
- Epstein M (1999), On the Wrinkling of Anisotropic Elastic Membranes, Journal of Elasticity 55, 99-109. Comments: The problem of wrinkling of elastic membranes has many applications, including the deployment of solar panels in space. The standard tension-field theory is here extended to anisotropic fabrics. The extension is far from trivial. It is achieved by showing that the wrinkling condition (namely, the appearance of compression) can be ingeniously understood in terms of the characteristic strips of a first-order non-linear PDE.
Epstein M (1999), On the Anelastic Evolution of Second-Grade Materials, Extracta Mathematicae 14/2, 157-161
Epstein M and Johnston C (1999), Improved Solution for Solitary Waves in Arteries, J. of Mathematical Biology 39, 1-18.
Wu J Z, Herzog W and Epstein M (1999), Modelling of Location-and-time-dependent Deformation of Chondrocytes During Cartilage Loading, Journal of Biomechanics 32, 563-572
Forcinito M, Epstein M and Herzog W (1999), Can a Rheological Muscle Model Predict Force Depression/Enhancement?, Journal of Biomechanics 31, 1093-1099
Epstein M (1999), On Material Evolution Laws, in Geometry, Continua and Microstructure, Collection Travaux en Cours 60, 1-10
Maugin G A and Epstein M (1998), Geometrical Material Structure of Elastoplasticity, International Journal of Plasticity 14, 109-115.
Epstein M. and de León M (1998), On Uniformity of Shells, Int. J. Solids Structures 35, 2173-2182.
Forcinito M, Epstein M and Herzog W (1998), A Numerical Study of the Stiffness of a Sarcomere, Journal of Electromyography and Kinesiology 8, 133-138
- Epstein M. and de León M (1998), Geometrical Theory of Uniform Cosserat Media, J. of Geometry and Physics 26, 127-170. Comments: Manuel de Leon is one of the most salient figures in the European mathematical scene. I was fortunate to succeed in arousing his interest in applications of differential geometry (his field of expertise) to solid mechanics. Among the many fruits of our collaboration, this major article introduces for the first time the notion of material groupoid.
Ru C Q, Mao X and Epstein M (1998), Electric-Field Induced Interfacial Cracking in Multilayer Electrostrictive Actuators, J. of the Mechanics and Physics of Solids 46, 1301-1318.
Wu J Z, Herzog W and Epstein M (1998), Articular Joint Mechanics with Biphasic Cartilage Layers Under Dynamic Loading, J. of Biomechanical Engineering 120, 77-84
Wu J Z, Herzog W and Epstein M (1998), Evaluation of the Finite Element Software ABAQUS for Biomechanical Modelling of Biphasic Tissues, J. of Biomechanics 31, 165-169
Epstein M and Slawinski M (1998), On Some Aspects of the Continuum-Mechanics Context, Revue de l’Institut Français du Pétrole 53, 669-677
Wu J Z, Herzog W, and Epstein M (1998), Effects of Inserting a Pressensor Film into an Articular Joints on the Actual Contact Mechanics, Journal of Biomechanical Engineering 120, 655-659.
Herzog W, Diet S, Suter E, Mayzus P, Leonard T R, Muller C, Wu J Z and Epstein M (1998), Material and functional properties of articular cartilage and patellofemoral contact , Journal of Biomechanics, Dec 1998.
- Forcinito M, Epstein M and Herzog W (1997), Theoretical Considerations on Myofibril Stiffness, Biophysical Journal 72, 1278-1286. Comments: Working in collaboration with Walter Herzog, whose Human Performance Laboratory is one of the best in the world, we provide a discrete model for sarcomeres (the basic units of skeletal muscle) that takes into account the compliance of the myofilaments. The limiting case of an infinite ladder of filaments is shown to approximate a preexistent continuous model.
Wu J Z, Herzog W and Epstein M (1997), An Improved Solution for the Contact of Two Biphasic Cartilage Layers, J. Biomechanics 30/4, 371-375
Epstein M and de León M (1997), Uniformidad Material de Vigas Alabeadas, Anales de Ingeniería Mecánica 3, 539-545
Epstein M and de León M (1996), Homogeneity Conditions for Generalized Cosserat Media, Journal of Elasticity 43, 189-201.
de León M and Epstein M (1996), The Geometry of Uniformity in Second-Grade Elasticity, Acta Mechanica 114, 217-224.
Epstein M and Maugin G A (1996), On the Geometrical Material Structure of Anelasticity, Acta Mechanica 115, 119-131.
Segev R and Epstein M (1996), On Theories of Growing Bodies, in Contemporary Research in the Mechanics and Mathematics of Materials (CIMNE), Eds. R.C. Batra and M.F. Beatty, Barcelona, 119-130
Epstein M. and de León M(1996), Uniformity and Homogeneity of Elastic Rods, Shells and Cosserat Three-Dimensional Bodies, Archivum Mathematicum (Brno)
Epstein M and de León M (1996), The Differential Geometry of Cosserat Media, in New Developments in Differential Geometry (Kluwer), Math. Appl. 350, 143-164
Epstein M. and de León M (1996), Uniformity and Homogeneity of Deformable Surfaces, C.R. Acad. Sci. Paris 323, Série II b, 579-584
Epstein M and de León M (1996), Geometric Characterization of the Homogeneity of Media with Microstructure, Extracta Mathematicae 11, 116-126
Allinger T L, Herzog W and Epstein M (1996), Force-Length Properties in Stable Skeletal Muscle Fibres - Theoretical Considerations, Journal of Biomechanics 29, 1235-1240
Epstein M and Maugin G A (1996), Geometrical Material Structure of Finite Strain Elasticity and Anelasticity, Zeit. Angew. Math. Mech. 76 (S4), 125-128
Allinger T L, Herzog W and Epstein M (1996), Stability of Muscle Fibres on the Descending Limb of the Force-Length Relation: A Theoretical Consideration, Journal of Biomechanics 29, 627-633
Epstein M and Maugin G A (1995), Thermoelastic Material Forces: Definition and Geometric Aspects, C.R. Acad Sci Paris, II-320, 63-68.
Forcinito M and Epstein M (1995), Granular Media Model with Internal Structure, Physica D 81, 305-313.
Cohen H and Epstein M (1994), On a Class of Planar Motions of Flexible Rods, Journal of Applied Mechanics 61, 206-208.
Epstein M (1994), On the 'Original' Septuagint, The Bible Translator 45, 323-329.
De León M and Epstein M (1994), Material Bodies of Higher Grade, C.R. Acad Sci Paris I-319, 615-620
Epstein M and de León M (1994), Dislocaciones Distribuidas en Medios Elásticos, Anales de Ingenieria Mecanica 2, 577-583
Epstein M (1994), Thoughts on Humanistic Engineering, Bulletin of the Canadian Society for Mechanical Engineering, November issue,.6-11
De León M and Epstein M (1993), On the Integrability of Second-Order G-Structures with Applications to Continuous Theories of Dislocations, Reports on Mathematical Physics 33, 419-436
Epstein M and Sniatycki J (1992), Fermat's Principle in Elastodynamics, J. of Elasticity 27, 45-56
Maugin G A, Epstein M and Trimarco C (1992), Pseudomomentum and Material Forces in Inhomogeneous Materials, International Journal of Solids and Structures 29, 1889-1900
Maugin G A, Epstein M and Trimarco C (1992), Theory of Elastic Inhomogeneities in Electromagnetic Materials, International Journal of Engineering Science 30, 1441-1449
Elzanowski M and Epstein M (1992), The Symmetry Group of Second-Grade Materials, Int. J. of Non-Linear Mechanics 27, 635-638
- Maugin G A and Epstein M (1991), The Electroelastic Energy-Momentum Tensor, Proc. Royal Soc. London A433, 299-312. Comments: This paper demonstrates how the theory of configurational forces in continuous media can be extended non-trivially to applications in the realm of dielectric materials.
Elzanowski M and Epstein M (1991), The Interplay of Uniformity with Constrained Elasticity, Stability and Applied Analysis of Continua 1/1, 95-107
Epstein M and Maugin G A (1991), Energy-Momentum Tensor and J-integral in Electrodeformable Bodies, International Journal of Applied Electromagnetics in Materials 2, 141-146
Epstein M. et Maugin G A (1990), Sur le Tenseur de Moment Materiel d'Eshelby en Elasticité non-lineaire, C R Acad. Sci. Paris II 310, 675-678.
- Epstein M and Maugin G A (1990), The Energy-Momentum Tensor and Material Uniformity in Finite Elasticity, Acta Mechanica 83, 127-133. Comments: In this paper, we established the surprising connection between the Eshelby stress (driving the motion of dislocations) and the notion of material isomorphism in elastic materials. This connection provides the foundation for the formulation of properly covariant laws of material evolution.
Elzanowski M, Epstein M and Sniatycki J (1990), G-structures and Material Homogeneity, Journal of Elasticity 23, 167-180.
Elzanowski M and Epstein M (1990), Propagación de ondas en elasticidad no-lineal, Sismodinamica 1, 45-55
Huttelmaier H P and Epstein M (1990), A Large-Displacement Finite Element for Multilayered Plates, Finite Elements in Analysis and Design 6, 189-196
Huttelmaier H P and Epstein M (1989), A Multilayered Finite Element Formulation for Vibration and Stability Analysis of Plates, ASCE Journal of the Engineering Mechanics Division 115/2, 315-325
Elzanowski M, Sniatycki J and Epstein M (1989), Geometry of Uniform Materials, Geometry and Topology, (ed. M. Raffias and G.M. Stratopoulos, World Scientific), 134-151
Elzanowski M and Epstein M (1989), On Uniformity and Homogeneity of Elastic Materials with Internal Constraints, in Continuum Mechanics and its Applications (ed. G.A.C. Graham and S.K. Malik, Hemisphere), 51-57
Elzanowski M and Epstein M (1988), The Decay and Formation of One-dimensional Nonconservative Shocks, Applied Mathematical Modelling 12/3, 280-284
Epstein M (1987), A Question of Constant Strain, Journal of Elasticity 17, 23-34
Elzanowski M and Epstein M (1986), Attenuation of Shocks by Viscoelastic Support, ASCE Journal of the Engineering Mechanics Division 112/6, 587-592
Dost S and Epstein M (1986), One-dimensional Nonlinear Shock Waves in Rigid Dielectrics, Bulletin of the Technical University of Istanbul 39, 33-40.
Elzanowski M and Epstein M (1985), Geometric Characterization of Hyperelastic Uniformity, Archive for Rational Mechanics and Analysis 88, 347-357
Epstein M and Gozde S (1985), On Exceptional Waves in Membranes, SM Archives 10, 87-99
Huttelmaier H P and Epstein M (1985), A Finite Element Formulation for Multilayered and Thick Shells Computers and Structures 21/6, 1181-1185
Elzanowski M and Epstein M (1985), Decay of Strong Shocks in Nonlinear Elasticity, Journal of Sound and Vibration 103/3, 371-378
Epstein M, Elzanowski M and Sniatycki J (1985), Locality and Uniformity in Global Elasticity, in Lecture Notes in Mathematical Physics 1139, Springer Verlag
Cohen H and Epstein M (1984), Remarks on Uniformity in Hyperelastic Materials, International Journal of Solids & Structures 20/3, 233-243
Cohen H and Epstein M (1983), Homogeneity Conditions for Elastic Membranes, Acta Mechanica 47, 207-220
Epstein M and Huttelmaier H P (1983), A Finite Element Formulation for Multilayered and Thick Plates, Computers and Structures 16, 645-650
Cohen H and Epstein M (1983), A Note on Nonlinear Elastic Wave Propagation, Mechanics Research Communications 10, 37-44
Cohen H and Epstein M (1982), Wave Fronts in Elastic Membranes, Journal of Elasticity 12, 249-263
Epstein M and Glockner P G, Deep and Multilayered Beams, ASCE Journal of the Engineering Mechanics Division 107/EM6, 1029-1037
- Epstein M and Segev R (1980), Differentiable Manifolds and the Principle of Virtual Work in Continuum Mechanics, Journal of Mathematical Physics 21, 1243-1245. Comments: I had the privilege of supervising the doctoral work of Reuven Segev, now a prominent figure in the field of continuum Physics. In this early work, which has become a game changer in the field, we provide the basis for the extension of classical analytical mechanics to the infinite dimensional case.
Epstein M and Glockner P G (1980), On Non-Isothermal Rigid Shell Theory, ZAMM 60, 65-70
Cohen H and Epstein M (1979), Acceleration Waves in Constrained Elastic Rods, Archive for Rational Mechanics and Analysis 72, 141-154.
Epstein M and Glockner P G (1979), Multilayered Shells and Directed Surfaces, International Journal of Engineering Science 17, 553-562.
Epstein M (1979), Thin-Walled Beams as Directed Curves, Acta Mechanica 33, 229-242.
Epstein M (1979), A Note on Nonlinear Compatibility Equations for Sandwich Shells and Cosserat Surfaces, Acta Mechanica 31, 285-289
Chowdhury K L, Epstein M and Glockner P G (1979), On the Thermodynamics of Nonlinear Elastic Dielectrics, International Journal of Nonlinear Mechanics 13, 311-322
Epstein M, Nixon D and Murray D W (1978), Large Displacement Inelastic Analysis of Beam-Columns, ASCE Journal of the Structural Division 104/ST5, 841-853
Epstein M and Murray D W (1978), A Biaxial Constitutive Law for Concrete Incorporated in BOSOR5 Code, Computers and Structures 9, 57-68
Epstein M (1978), Waves in Constrained Materials and Thin-Walled Beams, ASCE Journal of the Engineering Mechanics Division 104/EM5, 1213-1228
Epstein M and Glockner P G (1977), Nonlinear Analysis of Multilayered Shells, International Journal of Solids and Structures 13, 1081-1089
Epstein M and Murray D W (1976), Large Deformation In-Plane Analysis of Elastic Beams, Computers and Structures 6, 1-9
Epstein M and Murray D W (1976), Three-Dimensional Large Deformation Analysis of Thin-Walled Beams, International Journal of Solids and Structures 12, 867-876
Tene Y, Epstein M and Sheinman I (1975), Dynamics of Curved Beams Involving Shear Deformation, International Journal of Solids and Structures 11, 827-840
Tene Y, Epstein M and Sheinman I (1974), A Generalization of Potters' Method, Computers and Structures 4, 1099-1103
Epstein M and Tene Y (1973), A Linear Theory of Thin Elastic Shells, Based on Conservation of a Non-Normal Straight Line, International Journal of Solids and Structures 9, 257-268
Epstein M and Tene Y (1971), Nonlinear Analysis of Pin-Jointed Space Trusses, ASCE Journal of the Structural Division 97/ST9, 2189-2202
Selected expository presentations
Grassmann Statics, International Conference on The Multiscale Spectrum of Constitutive Modeling in Solid Mechanics, July 1-5, 2019, Centro Internacional de Encuentros Matematicos, Castro Urdiales, Spain
A general modeling framework for phenomena of material evolution, Invited mini-symposium keynote at CMBBE 2019, 16th International Symposium on Computer Methods in Biomedical Engineering, Columbia University, August 14-16, 2019.
Differential Geometry and Continuum Mechanics, keynote address at the VII Congress of Applied, Computational and Industrial Mathematics, Rio Cuarto, Argentina, May 9, 2019.
Material Geometry, invited 1-hour presentation at the Dipartimento di Scienze Matematiche "G. L. Lagrange", Politecnico di Torino, February 16, 2018.
Geometry and Continua, invited 1-hour presentation at the Mathematics Department, University of Strathclyde, Glasgow, March 14, 2018.
Geometry and Continua, invited 1-hour presentation at the Mathematics Department, Heriot-Watt University, Edinburgh, March 16, 2018.
Why be a mathematician, Round-table chair, Workshop on Geometry and Mechanics, University of Victoria, Canada, July 16-20, 2018.
Participated, with an invited 30-minute presentation, in a week-long BIRS meeting (Banff Centre, December 10-15, 2017). Details: BIRS Workshop 17w5164 - Mathematics for Developmental Biology. Presentation Topic: Growth, remodeling, aging and morphogenesis within the continuum mechanics context.
Co-organized and participated, with a 60-minute presentation, in a week-long BIRS meeting (Banff Centre, June 11-18, 2017). Details: BIRS Workshop 17frg674 - Material Evolution from plasticity to morphogenesis. Presentation Topic: Material Geometry.
Encounters, or The Joy of Texts. Date: February 2, 2016. Invited by: The Apeiron Society of philosophy, Calgary. Duration of talk: 1 hour.
A modeler’s lament. Date: March 5, 2015. Venue: Human Performance Laboratory, U of C. One-hour invited presentation at the HPL Seminar Series.
Material groupoids in remodeling and aging. Date: June 3, 2015. Venue: Mathematics Department, Politecnico di Milano. 1-hour invited presentation, hosted by Profs. Davide Ambrosi and Maurizio Vianello.
Material groupoids in remodeling and aging. Date: November 6, 2015. Venue: Mathematics Department, University of Pittsburgh. 1-hour seminar hosted by Prof. Anna Veinchtein
Differential Geometry and Continuum Mechanics. Date: November 6, 2015. Venue: Mathematics Department, University of Pittsburgh. 1-hour departmental colloquium.
Theoretical modeling of phenomena of remodeling, aging and growth. Date: October 13, 2015. Venue: Korea Institute of Industrial Technology, Seoul, Korea. 1-hour seminar hosted by Dr. Sang-Kuy Han
Differential geometry in continuum mechanics. Date: February 17, 2014. Venue: MEMOCS (International Research Center for Mathematics & Mechanics of Complex Systems), Universita dell’Aquila, Cisterna di Latina, Italy. This 1-hour seminar was in part a competition towards the Levi-Civita Prize, which was officially awarded to me in the 17th US National Congress on Theoretical and Applied Mechanics, that took place later, June 10-14, 2014, in Michigan State University, East Lansing, Michigan.
Invited mini course on Differential Geometry, ICMS Workshop on Differential Geometry and Continuum Mechanics, Edinburgh. Two 50-minute lectures, June 16 and 17, 2013
Keynote lecture, at the Mechanics – New Challenges ISIMM Symposium, Technion, Haifa, September 3, 2012. Topic: Remodeling and Growth. Duration: 45 minutes.
Invited Seminar, Oxford Centre for Collaborative Applied Mathematics (OCCAM), Title: The case for Differential Geometry in Continuum Mechanics, Date: November 16. 2010. Duration: 1 hour.
Invited Seminar, Department of Mechanical Engineering, University of California San Diego, Title: The split between remodeling and aging, Date: June 15, 2009. Duration: 1 hour.
Invited Seminar, Universidad de Buenos Aires, IMATEC, Title: Geometría, Inhomogeneidad y Evolución Material, Date: June 27, 2008. Duration: 1hr.
Invited Seminar, Institut Jean Le Rond d'Alembert, Series: Séminaires de Mécanique des Solides, Title: Elementary Fractal Mechanics, Date: May 27, 2008. Duration: 1hr.
“Algunas aplicaciones de la geometría diferencial a la mecánica de los medios continuos”, invited 1-hour presentation at the Mathematics Department, Universidad del Sur, Bahía Blanca, Argentina, May 29, 2006.
Invited Seminar, Invited by the University of La Habana, Cuba. Title: "Mechanics of Fractal Media". Date: December 13, 2006. Duration: 1hr.
Invited Seminar, Invited by McGill University for the series: "Seminars in Mechanics". Title: Fractal Mechanics. Date: November 30, 2006. Duration: 1hr.
Advanced Continuum Mechanics for Mathematicians, 19th International Workshop on Differential-geometric Methods in Theoretical Mechanics, Bedlewo, Poland, 26/09/2004, Invited, 3-hour invited presentation at the Banach International Mathematical Center.
“Nonlocal Configurational Entities”, invited 50-minute presentation at the SNP Meeting on Multiscale Effects in Material Microstructures and Defects, University of Kentucky, Lexington, KY, September 27, 2003.
"Fluxes through strange Boundaries", invited 45-minute lecture at the Accademia Nazionale dei Lincei, Rome, October 15, 2002.
"The uses of Differential Geometry in the Mechanics of Deformable Media", Spotlight Lecture Series, The Pacific Institute for the Mathematical Sciences, Calgary, March 21, 2002.
“Uses and Abuses of Mathematics in Engineering”, invited 1-hour lecture at the International Symposium on Mathematics as the Conceptual Support of Science and Engineering, Fundacion Ramon Areces, CEAMM2000, Madrid, Spain, May 11-12, 2000.
“Who Invented Calculus?”, invited 1-hour talk at the Calgary XVIII-th Century Studies Group, Calgary, January 11, 2000.
“Second-Grade Evolution and Growth”, invited 1-hour seminar at the Mathematics Department, University of Pisa, June, 1998.
“On Material Evolution Laws”, invited 45-minute lecture at the International Seminar on Geometry, Continua and Microstructure, Paris, France, May 28-29, 1997.
“Moses Mendelssohn: From the Margins to the Mainstream”, invited 50-minute talk at the Symposium “Why XVIII-Century Studies?” organized by the Calgary XVIII-th Century Studies Group, Calgary, October 10-11, 1996.
Selected Conference Presentations
Epstein M, Material groupoids, algebroids and distributions, SIAM Conference on Mathematical Aspects of Materials Science, July 9 - 13, 2018, Portland, Oregon.
Epstein M, Some non-standard problems in the modeling of continuous distributions of defects, International Conference on Plasticity, Damage and Fracture, San Juan, Puerto Rico, January 3-9, 2018.
Spivak R and Epstein M, The Latin of Science, Annual conference of the Classical Association of Canada, Calgary, May 8-10, 2018.
Epstein M, Incompatibility in multi-walled nanotube composites, in Nonconvexity, Nonlocality and Incompatibility, Conference in honor of Lev Truskinovsky on the occasion of his 60th birthday, Mathematics Department, university of Pittsburgh, May 5-7, 2017. Invited 45 minute presentation.
Epstein M, Continuous defects in multi-walled nanotube composites, International Workshop on Modelling of Nonlinear Continua, Castro Urdiales, Spain, June 26-30, 2017. 30 minutes.
Alhasadi M F, Epstein M and Federico S, Eshelby stress and energy flow vector for uniform bodies, Proceedings of the 26th CANCAM, Victoria BC, May 29- June 1, 2017.
Participation by invitation in the Workshop (ID: 1729) on Material Theories (organizers: Sergio Conti (Bonn), Antonio DeSimone (Trieste), Stephan Luckhaus (Leipzig) and Lev Truskinovsky (Paris)), Mathematisches Forschungsinstitut Oberwolfach. Oberwolfach, Germany, July 16-22, 2017
Epstein M, A model for mechanically driven morphogenesis, 24th International Congress of Theoretical and Applied Mechanics (ICTAM24), Montreal, August 21-26, 2016. Duration of talk: 20 minutes.
Epstein M, What is a homogeneous shell? 6th Annual Conference on Civil Engineering, Athens Institute of Education and Research (ATINER), Athens, June 20-23, 2016. Duration of talk: 30 minutes.
Epstein M and de León M, Material groupoids and algebroids, XXV International Fall Workshop on Geometry and Physics, August 29 - September 2, 2016, Madrid, Spain. Duration of talk: 30 minutes.
Epstein M, Material Groupoids in Remodeling and Aging, International Workshop on Modeling Across the Biology-Mechanics Interface, September 1-4, 2015, Castro Urdiales, Cantabria, Spain. Duration of talk: 30 minutes.
Epstein M, From continuous to discrete dislocations, 2014 Symposium on New Developments in Defect Mechanics, January 2014. Venue: UCSD. Sponsored by the National Science Foundation (NSF). Abstracts published on the conference website (http://maeresearch.ucsd.edu/markenscoff/nsf/2014/NSF_Abstracts.pdf)
Duration of talk: 45 minutes.
Epstein M, Bridging between continuous and discrete dislocations, Conference Venue: ICMAT, Madrid. Conference in honour of Prof. M. de Leon on the occasion of his 60th birthday, December 2013. Duration of talk: 35 minutes. Abstracts and slides published at http://www.icmat.es/deLeonfest/programme.html.
Epstein M and Segev R, On the geometry of continuous and singular distributions of defects, Joint meeting: SES 50th Annual Technical Meeting and ASME-AMD Annual Summer Meeting, Brown University, Providence, RI, July 2013. Duration of talk: 20 minutes.
Cull S and Epstein M, A solid-fluid reacting mixture model for bone, Proceedings of the 49th Annual Technical Meeting of SES, Atlanta, Georgia, October 2012.
Epstein M and Goriely A, Mass self-diffusion, Book of Abstracts, ICMM2 Paris, August 31- September 2, 2011.
Epstein, M., The Field Equations of Surface Growth, presented at the BIRS Workshop on Mathematical Foundations of Mechanical Biology, Banff, September 26- October 1, 2010.
Epstein, M. and Segev, R., Notes on stresses in chains, Proceedings of ICTAM (20th International Congress of Theoretical and Applied Mechanics), August 23-28, 2008, Adelaide, Australia.
Epstein, M., Hidden quantities and qualities of Cosserat, Proceedings of Euromech 510 (Mechanics of Generalized Continua: A Hundred years after the Cosserats), Paris, May 13-16, 2009.
Epstein, M. and Adeeb, S., Fractal structural elements, Proceedings of PACAM X, January 7-11, 2008, Cancun, Mexico.
Epstein, M., A primer in inhomogeneity and growth, Report No. 58/2007, Mathematisches Forschungsinstitut Oberwolfach, Book of Abstracts of the meeting on Material Theories held in Oberwolfach, Germany, December 16-22, 2007 (A. de Simone, S. Luckhaus and L. Truskinovsky, eds.), p30.
Rouhi, G. R., Epstein, M. and Sudak, L, Modeling bone resorption using mixture theory, Book of Abstracts, 21st CANCAM held at Ryerson University, June 3-7, 2007, D. Naylor (ed.), Toronto, 2007
Epstein, M.; Adeeb, S.M. and Herzog, W. (2007). Dynamic loading and biological growth. American Society of Biomechanics (ASB) Annual Conference, August 22-25, Stanford University, San Francisco, California.
Epstein, M., Configurational balance and entropy sinks, presented at the International Symposium on Defect and Material Mechanics, March 25-29, 2007, Aussois, France
Epstein, M., Evolution of Material Inhomogeneity in General Relativity, Seventh International Seminar on Geometry, Continua and Microstructures, University of Lancaster, September 25-27, 2006
Epstein, M. and Sniatycki, J., Mechanics of Fractal Bodies, 43rd Annual Technical Meeting of the Society for Engineering Science (SES), University Park, Pennsylvania, August 13-16, 2006.
Shepit B., Epstein M., Tracking Control and the One-dimensional Heat Equation: a Differential Geometric Approach, Proceedings of the Eighth Pan-American Congress of Applied Mechanics (PACAM-VIII), La Habana, Cuba, January 2004, Pages 487-490, Refereed.
Rouhi GR, Epstein M., Herzog W, Sudak, L, Governing Equation of Bone Remodeling Process: Using Mixture Theory Approach, 13th Biennial Conference for the Canadian Society of Biomechanics, Halifax, Nova Scotia, Aug 4 –Aug 7. 2004 (Poster #9, Page 38 in the Proceedings).
Epstein M., The size of Elastic Wrinkles, Proceedings of the Eighth Pan-American Congress of Applied Mechanics (PACAM-VIII), La Habana, Cuba, January 2004, Pages 262-265, Refereed
Epstein, M., 2003 “Self-Driven Continuous Dislocations and Growth”, Euromech Colloquium 445, Mechanics of Material Forces, May 21-24, University of Kaiserslautern, Germany.
Epstein, M. and Sniatycki, J., 2003, “Global Eshelby Entities”, 40th Annual Technical Meeting of the Society for Engineering Science (SES), October 12-15, University of Michigan, Ann Arbor,
Epstein, M., “A course on Scientific Latin at the University of Calgary”, Classical Leanings, an Interdisciplinary Conference, Classical Association of the Canadian West, Simon Fraser University, Vancouver Campus, BC, February 22-23, 2002.
Epstein, M., “On some Aspects of Muscle Modelling”, Invited 30-minute presentation, Annual Meeting of the Society for Experimental Biology, University of Swansea, UK, April 8-12, 2002.
Elzanowski, M. and Epstein, M., “Remarks on Modelling the Evolution of Inhomogeneities”, STAMM 2002, STAMM2002, Symposium on Trends in Applications of Mathematics to Mechanics, Naples, September 29 - October 4, 2002.
Epstein, M. and Elzanowski, M., "A Model of the Evolution of a Two-dimensional Defective Structure", The Truesdell Symposium, 14th US National Congress of theoretical and Applied mechanics, Blacksburg, Virginia, June 23-29, 2002.
Epstein, M., "The Eshelby tensor and the theory of continuous distributions of inhomogeneities", Book of Abstracts, pp 67-68, MMC2001, 2001 Mechanics and Materials Summer Conference, San Diego, June 27-29, 2001.
Epstein, M., "The Eshelby stress within the theory of continuous distributions of inhomogeneities", Meeting of the Society for Natural Philosophy, Berkeley, September 28-October 1, 2000.
Epstein, M., "Material Geometry of Functionally Graded Bodies", ICTAM 2000-20th International Congress of Theoretical and Applied Mechanics, August 27- September 2, 2000, Chicago, Illinois.
Epstein, M., "The Relaxed Energy Function for Membrane Wrinkling and Saturated Elasticity", STAMM 2000 (P. E. O'Donoghue and J. N. Flavin, eds.), Proceedings of the 11th Symposium on Trends in Applications of Mathematics to Mechanics held in Galway, Ireland, July 9-14, 2000. Elsevier, pp. 66-71 (2000).
Epstein, M., “A Note on Wrinkling and Saturated Elasticity”, Contributions to Continuum Theories, Anniversary Vol. for Krzysztof Wilmanski, Report No. 18, Berlin 2000, pp. 73-76 (2000).
Epstein, M., "Continuous Distributions of Dislocations in Liquid Crystals?", 4th International Seminar on Geometry, Continua and Microstructure, Torino, 26-28 October 2000.
Johnston, C.R. and Epstein, M., “Solitary Wave Solution for Axially and Radially Deforming Arteries”, 4th International Congress on Industrial and Applied Mathematics. Edinburgh, Scotland. July 1999.
Epstein, M. and Maugin G.A., “Elements of a Theory of Growth”, Continuum Models and Discrete Systems (CMDS9), Proceedings of the 9th International Symposium, Editors: E. Inan & K.Z. Markov, Istanbul, Turkey, June 29-July 3, 1998, World Scientific Publishing Co., pp. 555-561 (1998).
Epstein, M. and Segev, R., "Theories of Growing Bodies", Book of Abstracts, ASME Mechanics and Materials Conference, The Ericksen Symposium, John Hopkins University, Baltimore, MD, June 12-14, p. 57 (1996).
Epstein, M., "Eshelby-Like Tensors in Thermoelasticity", in Nonlinear Thermodynamical Processes in Continua, W. Muschik and G.A. Maugin, eds., pp. 147-159, TUB-Dokumentation, Berlin (1992).
Elzanowski, M. and Epstein, M., "Coupled Shocks in Non-linear Elasticity", in Mathematical and Numerical Aspects of Wave Propagation Phenomena", (ed. G. Cohen, L. Halpern and P. Joly), pp. 519-524, SIAM (1991),
Epstein, M. and Maugin, G.A., "On the Energy-Momentum Tensor in Piezoelectricity", First Japanese-Polish Joint Seminar on Electromagnetic Effects in Deformable Solids and Materials, 9-12 April, 1990, Madralin, Poland.
Epstein, M., "Galileo's Two New Sciences", in Music and Science in the Age of Galileo, Conference Programme (ed. V. Coelho), 3-5, Calgary (1989).
Epstein, M., Elzanowski, M. and Sniatycki, J., "Remarks on Uniformity in Global Elasticity", 28th Meeting of the Society for Natural Philosophy, Lexington, Kentucky (1985).
Elzanowski, M. and Epstein, M., "Uniformity Characterization in Hyper-Elasticity", Proceedings of the XVIth IUTAM Congress, Lyngby, Denmark (1984).
Epstein, M. and Segev, R., "On the Principle of Virtual Work", in Abstracts of the XVth International Congress of Theoretical and Applied Mechanics, Toronto, 1980.
Epstein, M. and Glockner, P.G., "Multidirector Surface Theory: A Model for Layered Shells", Eighth U.S. National Congress of Applied Mechanics, U.C.L.A., (June 1978)
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