Ductile damage modelling of heterogeneous materials using a two-scale computational approach

Abstract

The paper presents a new two-scale methodology for modelling of damage in ductile heterogeneous materials employing homogenization approach over the two microstructural models. The first microstructural model comprises elastoplastic behaviour without softening, while only microstructural softening is homogenized in the second model. The scale transition of the state variables is based on the first-order computational homogenization scheme. The microstructural damage response is governed by the nonlocal variable embedded into the gradient elastoplastic formulation using the implicit localization approach. The averaging computation over the microstructural softening zones is driven by the damage variable and the local equivalent strain. Therein discretization is performed by using the mixed finite element formulation including the nonlocal equivalent plastic strain interpolation, while the standard displacement based finite elements, employing the simple constitutive relation with damage variable, are used at the macrolevel. The capability of modelling material damage responses at both the micro and macroscale is demonstrated by the benchmark examples.