Variational linear comparison bounds for nonlinear composites with anisotropic phases. II. Crystalline materials

作者：Idiart Martin I; Castaneda Pedro Ponte^*

来源：Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2007, 463(2080): 925-943.

DOI：10.1098/rspa.2006.1804

• nonlinear homogenization
• variational methods
• crystalline materials

In part I of this work, bounds were derived for the effective potentials of nonlinear composites with anisotropic constituents, making use of an appropriate generalization of the linear comparison variational method. In this second part, the special case of nonlinear composites with crystalline constituents is considered. First, it is shown that, for this special but very important class of materials, the `variational' bounds of part I are at least as good as an earlier version of the bounds due to deBotton & Ponte Castaneda. Then, the relative merits of these two types of bounds are studied in the context of a model, two-dimensional, porous composite with a power-law crystalline matrix phase, under anti-plane loading conditions. The results show that, indeed, the variational bounds of part I improve, in general, on the earlier bounds, with the former becoming progressively sharper than the latter as the number of slip systems of the crystalline matrix phase increases. In particular, it is shown that, unlike the bounds of deBotton & Ponte Castaneda, the variational bounds of part I are able to recover the variational bound for composites with an isotropic matrix phase, as the number of slip systems, all having the same flow stress, tends to infinity.

• 出版日期2007-4-8