The thermodynamically consistent formulation and the subsequent numerical implementation of a gradient-enhanced, continuum-coupled damage-plasticity model as a constitutive framework to model ill-posed localization problems is presented. The formulation of the elastoplastic-damage behavior of materials is introduced here within a framework that uses functional forms of hardening internal state variables in both damage and plasticity. Various exponential and power law functional forms are studied in this formulation. Gradients of hardening terms are found directly by operating on the respective hardening terms, and numerical methods are used to compute these gradients. The gradient-enhanced measure used in this work is justified by an approximation to nonlocal theory; however, through the expansion of various gradient terms in this nonlinear hardening plasticity model, gradients of both odd and even orders are introduced into the constitutive model. A multifield method is used such that the displacement field is interpolated using standard continuous elements, and higher-order elements (cubic Hermitian) are used for the plastic multiplier and for the damage multiplier to enforce continuity of the second-order gradients. The effectiveness of the model is evaluated by studying the mesh-dependence issue in localization problems through numerical examples.
展开▼
