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**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.

### MSC:

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 |