Microscale analysis of heterogeneous ductile materials with nonlocal damage models of integral type

A computational scheme for the analysis of damage localization in heterogeneous ductile materials in the case of non-separated scales is presented. The consistent linearization of nonlocal damage models of integral type at finite strains is addressed and the influence of nonlocal interactions on the homogenized material response is investigated. The constituents and phases of the material at the microstructural representative volume element (RVE) level are modeled with a nonlocal elasto-plastic isotropic damage model. The numerical integration of the constitutive equations within a nonlinear homogenization problem is described in detail. The scheme is applied to the simulation of ductile damage and the influence of the nonlocal averaging procedure, which can be evaluated at different configurations and include non-local interactions between different phases, is analysed. The quadratic rate of convergence of the Newton-Raphson iterative procedure is demonstrated and the capability to alleviate the pathological mesh dependence is illustrated through microstructural examples.