Evolution problems for a class of dissipative materials
Author:
Pierre-M. Suquet
Journal:
Quart. Appl. Math. 38 (1981), 391-414
MSC:
Primary 73E99; Secondary 49A29, 73F15
DOI:
https://doi.org/10.1090/qam/614549
MathSciNet review:
614549
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Abstract: This work examines the problems of dynamic and quasi-static evolution for a large class of dissipative materials, including viscoplastic, viscoelastic, and elastic perfectly plastic materials. We show that when the potential of dissipation is regular, the displacement solution is regular; however, in the case of perfect plasticity, where the potential is irregular, the solution can be discontinuous. A suitable framework is used in order to account for these discontinuities. Existence theorems are stated, and the boundary conditions are discussed. The evolution equations encountered in this work are strongly nonlinear but with a monotone time-dependent nonlinearity. A direct method of resolution is proposed, since the known results do not apply in this case.
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B. Halphen and Quoc Son Nguyen, Sur les matériaux standard généralisés, J. de Mécanique 14, 39–63 (1975)
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C. Johnson and B. Mercier, Une méthode pour résoudre le probléme de l’adaptation, C. R. Acad. Sc. Paris 283, 371–374 (1976)
N. Kenmochi, The semi-discretization method and nonlinear time-dependent parabolic variational inequalities, Proc. Jap. Acad. 50, 714–717 (1975)
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B. Mercier, Une méthode pour résoudre le probléme des charges limites, J. de Mécaniquue, 16 (1977)
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Article copyright:
© Copyright 1981
American Mathematical Society
