On the sensitivity of homogenized material responses at infinitesimal and finite strains

On a practical level, when computing macroscopic or homogenized mechanical responses of materials possessing heterogeneous irregular microstructure, o ne can only test finite-sized samples. The macroscopic responses computed f rom various equal finite-sized samples exhibit deviations from one another. Consequently, any use of such data afterwards contains a degree of uncerta inty. For example, certain classes of finite deformation response functions such as compressible Neo-Hookean functions, compressible Mooney-Rivlin fun ctions, and others, employ predetermined linear elastic coefficients in par ts of their representations. Therefore, they will contain the mentioned unc ertainties. In this work we study the magnitude of deviations between compu ted homogenized linearly elastic responses among equal finite sized, sample s possessing random microstructure. Afterwards, the sensitivity of finite d eformation response functions to such deviations is addressed. The primary result is that deviations of the responses in the infinitesimal range bound the resulting perturbed response in the finite deformation range from abov e. Copyright (C) 2000 John Wiley & Sons, Ltd.