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On micro–macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials. (English) Zbl 1112.74530

Summary: We introduce a two scale computational strategy for modeling the inelastic behavior of heterogeneous materials. We apply the FEM not only on the structural scale but also on the lower, so called micro scale, where it replaces the standard procedure, in which we define the material behavior through the constitutive relations. The special care is given to handling the interface condition between micro- and macro scales. The proposed approach is based on the localized Lagrange multiplier method and can lead to the realization of either displacement based or force based formulation. Numerical tests were done on porous and composite materials. We investigate the influence of the boundary conditions, micro scale representation window size and phase contrast on the heterogeneous material response of a single FE as well as of the whole structure.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E05 Inhomogeneity in solid mechanics
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
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