engleski

A novel multiscale approach in modeling of ductile damage in heterogeneous materials

Conventional homogenization approaches are not appropriate for the analysis of the softening of heterogeneous materials, because the averaging over whole representative volume element (RVE) cannot adequately describe localization phenomena. Another issue is that the increase in the RVE size leads to increased brittleness at the macroscale. There are some suggestions to overcome these problems, mostly for the brittle materials, where the converged results are obtained by averaging only over a loading zone where damage is rising. In this contribution, a multiscale model is proposed for the modelling of ductile damage in heterogeneous materials. For this purpose, the nonlocal implicit ductile damage model is employed at the microstructural level. Therefore, microlevel is discretized by the mixed quadrilateral finite elements with nonlocal equivalent plastic strain as a nodal degree of freedom. At the macrolevel, the standard plane strain quadrilateral finite elements are used for discretization. Two separate RVE analyses are performed at the microlevel, one is employed on the bulk, undamaged material, where the stress and constitutive operator are extracted using conventional homogenization and in another homogenization procedure the softening is captured by a novel approach, where the homogenized damage variable is computed. According to the multiscale computation technique, all homogenized variables are mapped to the macrolevel, where they are embedded into the finite element formulation. All algorithms derived are implemented into the FE software ABAQUS via user subroutines. The proposed computational model is verified using several benchmark examples.

damage, homogenization, multiscale analysis

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