Variational formulation for nonlocal damage models

International journal of plasticity

Volumn 15, Issue 2, 1999, Pages 119-138

  Lorentz, E ^a,b   Andrieux, S ^a  

^a EDF R AND D   (France)

^b Grande Voie des Vignes   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY VALUE PROBLEMS; FRACTURE; MATHEMATICAL MODELS; OPTIMIZATION; POROSITY; PROBLEM SOLVING; STRAIN; VARIATIONAL TECHNIQUES;

ENERGY METHODS; NONLOCAL DAMAGE MODEL;

PLASTICITY;

EID: 0032684607     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(98)00057-6     Document Type: Article

References (42)

1. Aïfantis E.C. The physics of plastic deformation. Int. J. Plas. 3:1987;211-247.
2. Anand L., Kim K.H., Shawki T.G. Onset of shear localization in viscoplastic solids. J. Mech. Phys. Solids. 35:(4):1987;407-429.
3. Andrieux, S., de Bonnières, P., 1994. Including thermal gradients into thermoelastic damage constitutive laws: a homogenization approach. Localized damage, Udine, 6/21/94-6/23/94.
4. Andrieux S., Joussemet M., Lorentz E. A class of constitutive relations with internal variable derivatives: derivation from homogenization. C. R. Acad. Sci. t. 323:(Série II b):1996;629-636.
5. Andrieux S., Lorentz E., Joussemet M. A class of constitutive relations with internal variable derivatives: initial value problem. C. R. Acad. Sci., t. 323:(Série II b):1996;571-578.
6. Bazant Z.P., Pijaudier-Cabot G. Nonlocal continuum damage, localization instability and convergence. J. Appl. Mech. 55:1988;287-293.
7. Bazant Z.P., Belytschko T.B., Chang T.P. Continuum theory for strain softening. J. Engng Mech. Div. ASCE. 110:1984;666-1692.
8. Benallal, A., Billardon, R., Geymonat, G., 1993. Bifurcation and localization in rate-independent materials. Some general considerations. In: Nguyen, Q.S., (Ed.), Bifurcation and Stability of dissipative Systems. Springer Verlag, Berlin, pp. 1-44.
9. Bui, H.D., 1978. Mécanique de la rupture fragile. Masson (Ed.), Paris.
10. Cherukuri H.P., Shawki T.G. An energy-based localization theory: I. basic framework. Int. J. Plas. 11:(1):1995;15-40.
11. Coleman B.D., Noll W. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Rat. Mech. Anal. 13:1963;167-178.
12. Cowin S.C., Nunziato J.W. Linear elastic materials with voids. J. Elasticity. 13:1983;125-147.
13. de Borst R., Mühlhaus H.-B. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Num. Meth. Eng. 35:1992;521-539.
14. Ekeland, I., Temam, R., 1974. Analyse convexe et problèmes variationnels. Dunod Gauthier-Villars, Paris.
15. Eringen A.C. Linear theroy of micropolar elasticity. J. Math. Mech. 15:1966;909-924.
16. Fedelich B., Ehrlacher A. An analysis of stability of equilibrium and of quasi-static transformations on the basis of the dissipation function. Eur. J. Mech., A/ Solids. 16:(5):1997;833-855.
17. Fortin, M., Glowinski, R., 1983. Augmented lagrangian methods: applications to the numerical solution of boundary value problems. In: Studies in Mathematics and its Applications, vol. 15. Elsevier.
18. Francfort G., Marigo J.-J. Stable damage evolution in a brittle continuous medium. Eur. J. Mech., A/Solids. 12:(2):1993;149-189.
19. Frémond M., Nedjar B. Damage in concrete : the unilateral phenomenon. Nucl. Eng. Des. 156:1995;323-335.
20. Germain P. The method of virtual power in continuum mechanics. Part 2 microstructure. SIAM J. Appl. Math. 25:(3):1973;556-575.
21. Germain P., Nguyen Q.S., Suquet P. Continuum thermodynamics. J. Appl. Mech. 50:(12):1983;1010-1020.
22. Hadamard, J., 1903. Leçon sur la propagation des ondes et les équations de l'hydrodynamique. Paris.
23. Halphen B., Nguyen Q.S. Sur les matériaux standards généralisé J. de Mécanique. 14:1975;39-63.
24. Hill R. Acceleration waves in solids. J. Mech. Phys. Solids. 10:1962;1-16.
25. Hill R., Hutchinson J.W. Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids. 23:1975;239-264.
26. Krajcinovic D. Damage Mechanics. Applied Mathematics and Mechanics. 41:1996;512-515.
27. Lemaitre, J., Chaboche, L-L., 1998. Mécanique des matériaux solides, Dunod, (Ed.), Paris.
28. Markov K. On a microstructural model of damage in solids. Int. J. Eng. Sci. 33:(1):1995;139-150.
29. Maugin G.A. Internal variables and dissipative structures. J. nonequilibrium thermodynamics. 15:1990;173-192.
30. Meftah, F., 1997. Thèse de doctorat, INSA Lyon, France.
31. Mindlin R.D. Microstructure in linear elasticity. Arch. Rat. Mech. Anal. 16:1964;51-78.
32. Mindlin R.D., Eshel N.N. On first strain gradient theories in linear elasticity. Int. J. Sol. Struct. 4:1968;109-124.
33. Mühlhaus H.-B., Aïfantis E.C. A variational principle for gradient plasticity. Int. J. Solids Structures. 28:(7):1991;845-857.
34. Needleman A. Material rate dependence and mesh sensitivity in localization problems. Comp. Meth. Appl. Mech. Eng. 67:1988;69-85.
35. Nguyen Q.S. Bifurcation and stability in dissipative media (plasticity, friction, fracture). Appl. Mech. Rev. 47:(1):1994;1-3.
36. Pijaudier-Cabot G., Burlion N. Damage and localisation in elastic materials with voids. Mech. Coh. Frict. Mat. 1:1996;129-144.
37. Rudnicki J.W., Rice J.R. Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids. 23:1975;371-394.
38. Simo J.C., Oliver J. An analysis of strong discontinuities induced by strain softening in rate-independent inelastic solids. Comp. Mech. 12:1993;277-296.
39. Suquet, P., 1982. Plasticité et homogénëisation, Thése de doctorat d'État, University Paris VI, France.
40. Svedberg T., Runesson K. A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage. Int. J. Plas. 13:1997;669-696.
41. Toupin R.A. Theory of elasticity with couple-stress. Arch. Rat. Mech. Anal. 17:1964;85-112.
42. Valanis K.C. A gradient theory of internal variables. Acta Mech. 116:1996;1-14.