Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation

A constitutive model for orthotropic elastoplasticity at finite plastic strains is discussed and basic concepts of its numerical implementation are presented. The essential features are the multiplicative decomposition of the deformation gradient in elastic and inelastic parts, the definition of a convex elastic domain in stress space and a representation of the constitutive equations related to the intermediate configuration. The elastic free energy function and the yield function are formulated in an invariant setting by means of the introduction of structural tensors reflecting the privileged directions of the material. The model accounts for kinematic and isotropic hardening. The associated flow rule is integrated using the so-called exponential map which preserves exactly the plastic incompressibility condition. The constitutive equations are implemented in a brick-type shell element. Representative numerical simulations demonstrate the suitability of the proposed formulations.