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Second-Order Computational Homogenization Approach Using Higher-Order Gradients at Microlevel

Realistic description of heterogeneous material behavior demands more accurate modeling at macroscopic and microscopic scales. To observe strain localization phenomena and material softening occurring at the microstructural level, an analysis on the microlevel is unavoidable. Multiscale techniques employing several homogenization schemes can be found in literature. Widely used second-order homogenization requires C1 continuity at the macrolevel, while standard C0 continuity has usually been hold at microlevel. However, due to the C1-C0 transition macroscale variables cannot be defined fully consistently. The present contribution is concerned with a multiscale second-order computational homogenization employing C1 continuity at both scales under assumptions of small strains and linear elastic material behavior. All algorithms derived are implemented into the FE software ABAQUS. The numerical efficiency and accuracy of the proposed computational strategy is demonstrated by modeling three point bending test of the notched specimen.

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

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