Consistent tangent matrices for density-dependent finite plasticity models (Q2755619)

The paper deals with boundary value problems for elasto-plastic density-dependent models developed within the constitutive framework of finite elasto-plasticity, based on the multiplicative decomposition of deformation gradient into its elastic and plastic components. The material behavior is described in the actual configuration. The isotropic hyperelastic behavior characterizes the Kirchhoff stress in terms of the elastic left Cauchy-Green tensor, with free energy dependent on elastic measure and internal variables. The yield function is dependent on the Kirchhoff stress tensor and on the stress-like conjugated internal variables. The evolution equations are associated with the yield function and characterizes the Lie derivative of the elastic measure with respect to the spatial velocity and time derivative of internal variables, although certain objective derivative would be preferred. NEWLINENEWLINEThe numerical applications proposed in the paper adopt density-dependent elasto-plastic models, involving yield functions and flow rule dependent on the Kirchhoff stress and density, but without internal variables. The authors proposed for the numerical time integration, based on the standard return-mapping algorithm, a new consistent tangent moduli for density-dependent plastic models. It has been proved that the presence of the density in the plastic equations does not change the standard backward Euler return mapping algorithm based on the exponential mapping, but the consistent tangent modulli are strongly influenced. The numerical analysis of boundary value problems concerns models with different degrees of computational difficulty: Drucker-Prager model, elliptic and cone-cap models. The cone-cap model used by the authors is defined in the general finite hyperelastic-plastic framework, without simplifying kinematic assumptions. The example with Prager-Drucker model shows that the proposed approach, i.e. the numerical time integration and consistent tangent moduli, is valid for Cauchy-based elasto-plastic models. The examples with elliptic and cone-cap models emphasize that the consistent tangent moduli also give quadratic convergence for general density-dependent constitutive law. The influence of neglecting the density part of the consistent tangent moduli has also been analysed.