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Two-scale homogenization for a model in strain gradient plasticity. (English) Zbl 1300.74008

Summary: Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by N. A. Fleck and J. R. Willis [J. Mech. Phys. Solids 52, No. 8, 1855–1888 (2004; Zbl 1122.74486)] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74G65 Energy minimization in equilibrium problems in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure

Citations:

Zbl 1122.74486
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References:

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