On the numerical integration of three-invariant elastoplastic constitutive models. (English) Zbl 1036.74007

Summary: We investigate the performance of a numerical algorithm for the integration of isotropically hardening three-invariant elastoplastic constitutive models with convex yield surfaces. The algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity, and on a return mapping in principal stress directions. Smooth three-invariant representations of Mohr-Coulomb model, such as Lade-Duncan and Matsuoka-Nakai models, are implemented within the framework of the proposed algorithm. Among the specific features incorporated into the formulation are the hardening/softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure. Isoerror maps are generated to study the local accuracy of the numerical integration algorithm. Finally, a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full-scale nonlinear finite element simulation.


74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics


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