On the Role of Inhomogeneities in the Deformation of Elastic Bodies

TLDR: In this article, the authors investigate the consequences of such an assumption and show that it is clearly inappropriate for many classes of inhomogeneous bodies, both qualitatively and quantitatively, with regard to local measures such as stresses and strains.

Abstract: It is quite common to approximate “mildly” inhomogeneous bodies as homogeneous bodies belonging to a certain constitutive class in view of the simplification that such an approximation accords. In this study, we investigate the consequences of such an assumption and we show that it is clearly inappropriate for many classes of inhomogeneous bodies. We choose specific boundary value problems to illustrate the fact that we could be grossly in error, both qualitatively and quantitatively, with regard to local measures such as stresses and strains. In the examples considered, we find that, for global quantities such as applied forces and moments, the error could be significant. Not only could the material parameters found from, say, an extension test and torsion test, which neglect the inhomogeneity of the body, be quite different from one that incorporates the inhomogeneity, but also the values for the material parameter in the homogenized approximation gleaned from these different experiments could be differ...