Holes/cracks/inclusions in magneto-electro-elastic composite laminates under coupled stretching-bending deformation

Abstract

For the general magneto-electro-elastic (MEE) composite laminates, not only the elastic, electric and magnetic effects but also the in-plane stretching and out-of-plane bending deformations would be all coupled together. Based upon the classical lamination theory and by suitably expanding all the elastic tensors to include the electric and magnetic effects as the responses in the 4th and 5th dimensions, we develop the expanded Stroh-like formalism for MEE laminates under coupled stretching-bending deformation, whose mathematical form is purposely arranged to be identical to the Stroh-like formalism for elastic laminates. With the expanded Stroh-like formalism the field solutions for an infinite MEE laminate with or without holes/cracks/inclusions are derived analytically. The loads we consider are (1) the generalized uniform stress resultants and bending moments at infinity, and (2) the generalized concentrated forces and moments at an arbitrary location. Here, the word “generalized” means that the forces/moments are mechanical as well as electric and magnetic. The beauty of the obtained solutions is that these analytical solutions preserve the mathematical form of their corresponding elastic solutions. The only difference is the content and size of the matrices and vectors involved in the mathematical expressions. These solutions for the general MEE laminates including all the possible coupling effects are presented the first time in the literature. The ones under concentrated forces/moments are also taken to be the fundamental solutions of boundary element method. The correctness of our solutions is then verified through the comparison between the analytical solutions and those calculated by the newly developed boundary element method.