Thermomechanics of volumetric growth in uniform bodies

International journal of plasticity

Volumn 16, Issue 7, 2000, Pages 951-978

  Epstein, Marcelo ^a   Maugin, Gérard A ^b  

^a UNIVERSITY OF CALGARY   (Canada)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION IN SOLIDS; ELASTICITY; STRAIN RATE; STRESSES; TENSORS; THERMODYNAMIC PROPERTIES; THERMOMECHANICAL TREATMENT;

ESHELBY STRESS; FIRST ORDER TRANSPLANT THEORY; STRESS TENSOR; VOLUMETRIC GROWTH;

GROWTH (MATERIALS);

EID: 0033750776     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(99)00081-9     Document Type: Article

References (32)

1. Cordero L.A., Dodson C.T.J., de Leon M. Differential Geometry of Frame Bundles. 1989;Kluwer, Dordrecht, the Netherlands.
2. Cowin C.S. Strain or deformation rate dependent finite growth in soft tissues. J. Biomechanics. 29:1996;647-649. (and references therein).
3. Cowin C.S., Hegedus H.D. Bone remodeling I. theory of adaptive elasticity J. Elasticity. 6:1976;313-326.
4. Cleja-Tigoiu, S., Maugin, G.A., 2000. Eshelby's stress tensors in finite elastoplasticity. Acta Mechanica (in press).
5. Elzanowski M., Epstein M. On the symmetry group of second-grade materials. Int. J. Non-linear Mech. 27:1992;638-695.
6. Epstein, M., 2000a. On material evolution laws. In: Geometry, Continua and Microstructure. Collection "Travaux en cours", Herman, Paris.
7. Epstein M., 2000b. Towards a complete second-grade evolution Law. Math. and Mech. Solids (in press).
8. Epstein M., de Leon M. The geometry of uniformity in second-grade elasticity. Acta Mechanica. 114:1996;217-224.
9. Epstein M., Maugin G.A. The energy-momentum tensor and material uniformity in Finite Elasticity. Acta Mechanica. 83:1990;127-133.
10. Epstein M., Maugin G.A. Some geometrical aspects of inhomogeneous elasticity. Flato M., Kerner R., Lichnorowicz A. Physics on manifolds (Y.Choquet-Bruhat Festschrift Symposium, Paris, 1992). 1994;331-335 Kluwer, Dordrecht.
11. Epstein M., Maugin G.A. Thermoelastic material forces. Definition and geometric aspects C. R. Acad. Sci. Paris. II-320:1995;63-68.
12. Epstein M., Maugin G.A. On the geometrical structure of anelasticity. Acta Mechanica. 115:1996;119-131.
13. Epstein M., Maugin G.A. Notions of material uniformity and inhomogeneity. Tatsumi T., Wantanabe E., Kambe T. Theoretical and applied mechanics (Proc. ICTAM'96, Kyoto). 1997;201-215 North-Holland-Elsevier, Amsterdam.
14. Kobayashi, S., Nomizu, K., 1967. Foundations of Differential Geometry, Vol. I. Interscience Publishers, New York.
15. Le K.C., Stumpf H. A model of elastoplastic bodies with continuously distributed dislocations. Int. J. Plasticity. 11:1996;611-628.
16. Lehmann Th. Thermodynamical foundations of large inelastic deformations of solid bodies including damage. Int. J. Plasticity. 7:1991;79-98.
17. de Leon M., Epstein M. On the integrability of second-order G-structures with applications to continuous theories of dislocations. Rep. Math. Phys. 33:1993;413-436.
18. Lubliner J. Plasticity Theory. 1990;McMillan, New York.
19. Mandel J. Plasticité Classique et Viscoplasticité (CISM Lecture Notes, Udine, Italy). 1971;Springer-Verlag, Vienna.
20. Maugin G.A. Material Inhomogeneities in Elasticity. 1993;Chapman and Hall, London.
21. Maugin G.A. Eshelby Stress Tensor in Elastoplasticity and Ductile Fracture. Int. J. Plasticity. 10:1994;393-408.
22. Maugin G.A. Material forces. concepts and applications ASME. Appl. Mech. Rev. 48:1995;213-245.
23. Maugin G.A. Canonical momentum and energy in elastic systems with additional state variables. C.R. Acad. Sci. Paris. 323-IIb:1996;407-412.
24. Maugin G.A., Epstein M. Geometrical material structure of elastoplasticity. Int. J. Plasticity. 14:1998;109-115.
25. Maugin G.A., Trimarco C. Pseudomomentum and material forces in nonlinear elasticity. variational formulations and application to brittle fracture Acta Mechanica. 94:1992;1-28.
26. Maugin G.A., Trimarco C. The dynamics of configurational forces at phase-transition fronts. Meccanica. 30:1995;605-619.
27. Noll W. Materially uniform simple bodies with inhomogeneities. Arch. Rat. Mech. Anal. 27:1967;1-32.
28. Rodriguez E.K., Hoger A., McCulloch A.D. Stress-dependent finite growth in soft elastic tissues. J. Biomechanics. 27:1994;455-467.
29. Segev R., Epstein M. On theories of growing bodies. Batra R.C., Beatty M.F. Contemporary research in the mechanics and mathematics of materials. 1996;119-130 I.M.N.E, Barcelona.
30. Taber L.A. Biomechanics of growth, remodeling and morphogenesis. ASME. Appl. Mech. Rev. 48:1995;487-545.
31. Truesdell C.A., Noll W. The nonlinear field theories of mechanics. Flügge S. Handbuch der physik. 1965;Bd.III/3 Springer-Verlag, Berlin.
32. Wang C.C. On the geometric structure of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations. Arch. Rat. Mech. Anal. 27:1967;33-94.