Cam-Clay plasticity part III: Extension of the infinitesimal model to include finite strains Original Research Article

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 as well as 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 implicitly in the space defined by the invariants of the elastic logarithmic principal stretches, which requires the solution at each stress point of no more than three simultaneous non-linear 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.