In this chapter, the infinitesimal theory of elasto-plasticity of Chap. 12 is generalized to finite strains. Two formulations are presented. The first one is based on a multiplicative decomposition of the deformation gradient into elastic and plastic parts and on hyperelastic stress-strain relations. The second formulation assumes an additive decomposition of the rate of deformation and hypoelastic constitutive relations. Numerical algorithms are presented for both theories. Although the hyperelastic-based plasticity formulation is more satisfying from a theoretical point of view, the rate models are still widely used in numerical analysis.
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