engleski

C1 Microlevel Second-Order Computational Homogenization

For more realistic description of mechanical behavior of heterogeneous materials advanced modeling techniques are required. This means that capturing microstructural physical phenomena includes incorporation of an analysis at the microlevel. In this frame, the multiscale techniques employing homogenization scheme offer several solutions. Most recently developed two-scale scheme employing secondorder homogenization requires C1 continuity at the macrolevel, while classical continuum is kept at the microlevel. However, due to C1-C0 transition consistency of macroscale variables is violated. In this paper a new multiscale second-order computational homogenization algorithm preserving C1 continuous boundary value problem at both scales. Small strains and linear elastic material behavior are adopted. Numerical implementation of the theory derived is done using FE software ABAQUS. Verification of the proposed multiscale scheme is demonstrated by modeling three point bending test of notched specimen in comparison to the C1-C0 homogenization scheme.

heterogeneous materials; C1 finite element; C1 continuity microlevel; second-order computational homogenization; gradient generalized periodic boundary conditions

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