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J.C. Simo, G. Meschke:
"A New Class of Algorithms for Classical Plasticity Extended to Finite Strains. Application to Geomaterials";
Computational Mechanics, 11 (1993), 253 - 278.

A recently proposed methodology for computational plasticity at finite strains is re-examined within the context of geomechanical applications and cast in the general format of multi-surface plasticity. This approach provides an extension to finite strains of any infinitesimal model of classical plasticity that retains both the form of the yield criterion and the hyperelastic character of the stress-strain relations. Remarkably, the actual algorithmic implementation reduces to a reformulation of the standard return maps in principal axis with algorithmic elastoplastic moduli identical to those of the infinitesimal theory. New results in the area of geomechanics include a fully implicit return map for the modified Cam-Clay model, extended here to the finite deformation regime, and a new semi-explicit scheme that restores symmetry of the algorithmic moduli while retaining the unconditional stability property. In addition, a new phenomenological plasticity model for soils is presented which includes a number of widely used models as special cases. The general applicability of the proposed methodology is illustrated in several geomechanical examples that exhibit localization and finite deformations.

Keywords: plasticity, soil, finite strains, Cam-Clay, algorithms, geomaterials, fem-implicity, return map, implicit integration, penetration, pile footing