Multibody contact of two-dimensional anisotropic elastic/piezoelectric/magneto-electro-elastic solids

A unified expression for the generalized two-dimensional linear anisotropic elastic, piezoelectric, and magneto-electro-elastic (MEE) solids is established to simplify the connection between these three different kinds of materials. Here, the two-dimensional assumption includes the most general cases that in-plane and anti-plane deformations are allowed to couple each other. Based upon this unified expression, in this paper a recently developed boundary element method (BEM) for contact of two anisotropic elastic bodies is extended to solve the problems of multibody contact in which the bodies can be any combination of anisotropic elastic, piezoelectric and MEE solids. When a special case of contact between multiple rigid punches and an anisotropic elastic, piezoelectric or MEE half-plane is considered, further reduction can be made by introducing three degrees of freedom (two rigid body translations and one rigid body rotation) for each punch. With this consideration, no meshes are required on the rigid punches. The usual contact modes of separation, stick, and slip all include the situation of conductor and insulator if any one of the multibody is piezoelectric or MEE. In other words, in this paper we successfully develop two BEMs to solve the generalized two-dimensional problems of multibody contact. One is for the general cases whose bodies can be any combination of anisotropic elastic, piezoelectric and MEE solids, and the other is for the special cases of multiple rigid punches indenting on an anisotropic elastic, piezoelectric or MEE half-plane.