Elastoplastic finite element analysis of soil problems with implicit standard material constitutive laws. (English) Zbl 0924.73258

Summary: A new class of materials called implicit standard materials is proposed. It allows to generalize Fenchel’s inequality, and then to recover flow rule normality, for non-standard materials. We can show that implicit standard materials method describes several behaviours with simpler manner. We apply this approach to soil mechanics in order to build a non-associated constitutive law as the experience suggests. In term of FEM, an algorithm based on Newton’s method is proposed. It allows to obtain a symmetric stiffness matrix in reverse to actual non-associated formulation. A bearing capacity problem is considered as numerical application. Some results and theorems are discussed.


74S05 Finite element methods applied to problems in solid mechanics
74L10 Soil and rock mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74L05 Geophysical solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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