Solids with non-spherical cavities: Simplified representations of cavity compliance tensors and the overall anisotropy
The authors consider a cavity in an infinite linear elastic solid under the assumption that in the absence of cavity the stress field would be uniform and equal to the stress field at infinity. Under given loads, the authors analyze cavity compliances that determine the contribution of the cavity to the overal strain. In general, the above compliances are characterized by fourth rank tensors \(H\). The authors identify the classes of pore shapes for which the characterization by tensors \(H\) can be reduced, with sufficient accuracy, to the description in terms of second rank symmetric tensors and certain scalar shape factors. These tensors and shape factors are explicitly found in terms of the cavity geometry. It is also shown that in the framework of non-interaction approximation, a solid with pores of certain geometries is orthotropic for any orientational distribution of such pores. In addition, the number of independent moduli is five or even four, in the case of cracks. Finally, the authors show that randomly oriented ellipsoids (overall isotropy) can be approximated, from the point of view of effective moduli, by certain equivalent spheroids.
scientific article; zbMATH DE number 1420151