Research On The Homogenization Of Layered Composites Coupled With Multi-physical Phenomena

With the rapid development of material science, layered materials like laminates are widely used in practice, and the overall properties or macroscopic effective properties of the materials are mainly concerned about in application. What's more, in application environment or through some function materials such as piezoelectric materials and magnetostrictive materials, there are often multi-physical coupling phenomena. It is significant to focus on these problems, and some investigations have been done in the paper.Plane layered composites coupled with multi-physical phenomena are taken as study objects. The investigations are based on mean-filed homogenization theory and the assumptions that the micro-structure is periodic and each layer is well bonded. The paper includes the following aspects:First, multi-physical phenomena are analyzed and treated as a combination of several single fields and corresponding coupled fields, and then the multi-physical phenomena are governed by a unifying constitutive equation with the help of a divergence-free vector field and a curl-free vector field. Second, based on the mean-filed homogenization and Hadamard interface continuous conditions, material homogenization process of this category is given and subsequently, the exacted general notations of macroscopic effective modulus that can fully characterize the effective properties of the material are derived. At last, thermal conductivity and elasticity are treated as uncoupled illustrative examples, then, piezoelectricity and piezomagnetoelectricity are shown as coupled examples to verify the rationality of the method and the validity of the general notations.Since the derived solutions are tensorial notations, which are brief, coordinate-free, thus, they are suitable for a general case, even a more complicated n-coupled multi-physical case. This provides a good way for the corresponding problem both theoretically and practically.