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Computational homogenization of porous materials of Green type. (English) Zbl 1309.74061
Summary: The constitutive response of porous materials is investigated computationally. For the solid phase elasto- plastic behavior of Green type is considered, i.e. an isotropic compressible yield criterion is assumed. A wide range of material parameters and porosities from 0.1 to 30 % are investigated by means of FEM simulations of periodic ensembles of spherical pores. The dilatation of the pores and of the compressible matrix are evaluated. It is found that a large part of the total dilatation is due to plastic volume changes of the solid phase. The asymptotic stress states of the simulations are compared to analytical predictions by W. Q. Shen et al. [“Approximate criteria for ductile porous materials having a Green type matrix: Application to double porous media”, Comput. Mater. Sci. 62, 189–194 (2012; doi:10.1016/j.commatsci.2012.05.021)]. Based on the computational data, an effective constitutive law is proposed and verified by means of additional computations. A three-scale homogenization procedure for double porous materials is proposed that depends only on the micro- and mesoscale porosity and the yield stress of the solid phase.

MSC:
74Q05 Homogenization in equilibrium problems of solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
Software:
Netgen
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