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Cam-Clay plasticity. III: Extension of the infinitesimal model to include finite strains. (English) Zbl 0959.74010

[For part I see the first author and S. R. Lee, ibid. 78, No. 1, 49-72 (1990; Zbl 0718.73034); for part II see the first author, ibid. 88, No. 2, 225-240 (1991; Zbl 0746.73008).]
Summary: The infinitesimal version of the modified Cam-Clay model of critical state soil mechanics is reformulated to include finite deformation effects. Central to the formulation are the choice of a hardening law that is appropriate for cases involving large plastic volumetric strains, and the use of a class of two-invariant stored energy functions appropriate for Cam-Clay-type models that includes, as special cases, the constant elastic shear modulus approximation and the pressure-dependent shear modulus elastic model. The analytical model is cast within the framework of finite deformation theory based on a multiplicative decomposition of the deformation gradient. For the fully elasto-plastic case, return mapping is done implicitiy in the space defined by the invariants of elastic logarithmic principal stretches, which requires the solution at each stress point of no more than three simultaneous nonlinear equations. A finite element analysis of a strip footing problem is presented to illustrate a prototype example where finite deformation effects significantly impact the predicted response.

MSC:

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74L10 Soil and rock mechanics
74S05 Finite element methods applied to problems in solid mechanics
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