Fields of Interest:

 

  • Mathematical theory of defects

 

  • G-structures, frame bundles, theory of connections

 

  • Lie groups and algebras, classification, the equivalence

 

  • Hyperbolic waves, shock waves in non-linear elasticity

 

  • Cavitations in non-linear elasticity

 

  • Thermodynamics

 

 

Books, Notes:

 

·       (with G. P. Parry), A kinematics of defects in solids, in: Geometric Continuum Mechanics, Reuven Segev and Marcelo Epstein (eds), Birkhäuser/Springer, Berlin, 2020, https://www.springer.com/us/book/9783030426828

 

  • (with M. Epstein) Material Inhomogeneities and Their Evolution, A Geometric

Approach, Springer-Verlag, 2007, http://www.springer.com/978-3-540-72372-1

·       Mathematical Theory of Uniform Elastic Structures, Kielce University of Technology Press, Kielce, 1995. (PDF)

Selected Research Articles:

         

1.     (with M. Epstein) Material evolution of defective composites, Mathematics and Mechanics of Solids, Published online July (2023) https://doi.org/10.1177/10812865231185744

2.     Geometric characterization of continuously defective elastic crystals, Mathematics and Mechanics of Solids 27(7) (2022) 1212-1221, Published online December (2021) https://journals.sagepub.com/doi/full/10.1177/10812865211058769 (PDF)

3.     Torsion and curvature in continuously defective solid crystals, Atti della Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali, 99(1) (2021),  https://doi.org/10.1478/AAPP.991A3

4.     (with Gareth P. Parry) Connection and curvature in crystals with non-constant dislocation density, Mathematics and Mechanics of Solids, 24(6) (2019) 1714-1725. Published online August (2018), https://doi.org/10.1177/1081286518791008

5.     (with S. Preston) Continuously Defective Crystals with a Prescribed Defectiveness, International J. Geometric Methods in Modern Physics, 11(9) (2014).

6.     (with S. Preston) On Continuously Defective Elastic Crystals, Miskolc Mathematical Notes, 14(2) (2013) 659-670.

7.     (with S. Preston) Material Uniformity and the Concept of the Stress Space, in: Continuous Media with Microstructure, ed. B. Alberts, Springer-Verlag (2010) 91-101. (PDF),  http://www.springer.com/engineering/book/978-3-642-11444-1

8.     (with S. Preston)  A Model of the Self-Driven Evolution of a Defective Continuum, Mathematics and Mechanics of Solids, 12 (2007) 450-465. (PDF)

9.     (with G. P. Parry) Material Symmetry in a Theory of Continuously Defective Crystals, Journal of Elasticity, 74 (2004) 215-237. (PDF)

10.  (with M. Epstein )  A Model of the Evolution of a Two-dimensional Defective Structure, Journal of Elasticity, 70 (2003) 255-265. (PDF)

11.  (with E. Binz) Another Look at the Evolution of Material Structures, Mathematics and Mechanics of Solids, 7(2) (2002) 203-214. (PDF)

12.  About Non-Spherically Symmetric Deformations of an Incompressible Neo-Hookean Sphere, in: Contributions to Continuum Theories (Anniversary Volume for Krzysztof Wilmanski)  WIAS, (2000) 68-72 .  (PDF)

13.  (with S. Preston) On Non-Holonomic Second Order Connections, with Applications to Continua with Microstructure,  Extracta Mathematicae 11(1) (1996) 51-58. (PDF)

14.  (with S. Prishepionok)   Connections on Higher Order Frame Bundles in: New Developments in Differential Geometry, eds. L.Tamassy  and J.Szenthe, Kluwer Acad. Publishers (1996) 131- 142.  (PDF)

15.  (with S. Prishepionok)  Higher Grade Material Structures, Proceedings of the IUTAM & ISIMM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, University of Nottingham, August/September 1994, Kluwer (1995) 63-68.

16.  Some New Ideas in the Theory of Continuous Distributions of Defects, in: Characterization of Mechanical Properties of Materials, eds. W.-Y. Lu, C.-S. Man, ASME-MD, 33 (1992) 75-82.

17.  (with S. Prishepionok) Locally Homogeneous Configurations of Uniform Elastic Bodies, Reports on Mathematical Physics 31(3), (1992) 229-240.

18.  (with M. Epstein) The Symmetry Group of Second Grade Materials, International J. Non- linear Mechanics, 27(4), (1992) 635-638.

19.  (with M. Epstein) The Interplay of Uniformity and Constrained Elasticity, Stability and Applied Analysis of Continuous Media, 1, (1991) 95-107.

20.  (with M. Epstein and J.  Sniatycki) G-structures and Material Homogeneity, Journal of Elasticity, 23(2-3), (1990) 167-180.

21.  (with M. Epstein) The Decay and Formation of One-Dimensional Nonconservative Shocks, Applied Mathematical Modelling 12(3), (1988), 280-284.

22.  (with M. Epstein) Attenuation of Shocks by Viscoelastic Support, ASCE Journal of Engineering Mechanics, 112(6), (1986), 587-592.

23.  (with M. Epstein) Decay of Strong Shocks in Nonlinear Elasticity, Journal of Sound and Vibration, 103(3), (1985), 371-378.

24.  (with M. Epstein), Geometric Characterization of Hyperelastic Uniformity, Archive for Rational Mechanics and Analysis, 88, (1985), 347-357.

25.  Thermodynamic Stability of Continuous Body, Journal of Mathematical Analysis and Applications 108(2), (1985), 303-315

26.  On the Necessary Conditions for Stability in Thermodynamics, Bull.Acad.Polon.Sci. (Ser.Sci.Techn.) 28, (1980), 77-83.

 Updated March 25, 2021