In order to characterize the macroscopic behavior of a microscopically heterogeneous material, a homogenization methodology is typically employed where a micromechanical sample is identified and tested. See Refs. 1,2,3,4 for details and extensive references. This micromechanical testing (micro-to-macro transition) procedure for solids at finite deformations is governed by certain criteria. The fundamental criterion to be satisfied is a micro-macro work balance in the incremental form
$⟨P⋅dF⟩V0=P¯⋅dF¯$
1
that will be referred to as the work criterion. Here, the macroscopic first Piola–Kirchhoff stress tensor $P¯$ and the macroscopic deformation gradient $F¯$ are the fundamental macroscopic kinetical and kinematical measures that are used to construct all remaining measures via the usual continuum mechanics relationships and they are defined...
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