engleski

Multiscale modelling of deformation processes of nodular cast iron

In recent years, a special attention has been paid to investigate relations between the microstructure and mechanical properties of materials since almost all materials used in engineering are micro-heterogeneous. It is well-known that the classical continuum mechanics does not consider structural effects in the material at the micro-level. To overcome this problem, multiscale techniques have been developed for modelling of macroscopic behaviour of heterogeneous materials where the results obtained by analysis of a representative volume element (RVE) (micro-level) are used as an input to the continuum model (macro-level). To solve the problem at the micro-level the finite element (FE) method is mostly applied. To obtain more accurate results second order homogenization algorithm is applied. The aforementioned algorithm is derived for the plane stress and plane strain state assuming the elastoplastic behaviour of the material constituents. For the computational homogenization purposes on macro-level, a strain gradient finite element with C1 continuity is applied. The finite element and computational homogenization algorithm derived are implemented into the FE program ABAQUS/Standard using user-defined subroutines. In order to verify the FE formulation, several benchmark examples available in the literature are considered.

multiscale; second order homogenization; C1 finite element; nodular cast iron; Abaqus

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