On Ductile Damage Modelling of Heterogeneous Material Using Second-Order Homogenization Approach

Abstract

The paper deals with the numerical modelling of ductile damage responses in heterogeneous materials using the classical second-order homogenization approach. The scale transition methodology in the multiscale framework is described. The structure at the macrolevel is discretized by the triangular C1 finite elements obeying nonlocal continuum theory, while the discretization of microstructural volume element at the microscale is conducted by means of the mixed type quadrilateral finite element with the nonlocal equivalent plastic strain as an additional nodal variable. The ductile damage evolution at the microlevel is modelled by using the gradient enhanced elastoplasticity. The macrolevel softening is governed by two criterions expressed by the increase in homogenized damage variable and the threshold of the local equivalent strain. The softening at each material point at the macrolevel is detected by the critical value of the homogenized damage, where homogenization of the damage variable is performed only within softening area. Due to the nonlocal continuum theory applied, a realistic softening behaviour is demonstrated after the damage initiation, compared to the widely used first-order homogenization approach. All algorithms derived have been embedded into the finite element code ABAQUS by means of the user subroutines and verified on the standard benchmark problems. The damage evolution at both microlevel and macrolevel has been demonstrated.