engleski

A Homogenization Approach in Multiscale Modelling of Ductile Damage in Heterogeneous Materials

Standard homogenization techniques performing averaging over the whole representative volume element (RVE) are not well suited for the analysis of its softening response. The problem is relying in the phenomenological behaviour during softening, when a narrow localization zone is governing all the relevant microstructural mechanisms, while the rest of material remains unloaded. This also reveals important issue of the RVE representativeness. It has been shown that increase in the RVE size leads to increased brittle response at the macroscale. The problems mentioned are successfully overwhelmed for the softening of brittle materials. In this contribution, a new multiscale model is proposed for the modelling of ductile damage in heterogeneous materials. At the microstructural level, the nonlocal implicit ductile damage model is employed, where discretization is performed by means of the mixed quadrilateral finite elements. At the macrolevel, the 4-node plane strain quadrilateral finite elements, employing damage variable, are used. Two separate RVE analyses should be performed at the microlevel. First analysis is carried out on the undamaged material, where the homogenized stress and constitutive operator are obtained using the conventional first-order homogenization. In another RVE analysis, which includes softening, the homogenized damage variable is computed. Afterwards, all homogenized variables are mapped to the macrolevel. All algorithms derived are implemented into the FE software ABAQUS. The proposed computational model is verified on the usual examples.

damage, homogenization, multiscale analysis

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