Indentation by multiple rigid punches on two-dimensional anisotropic elastic or viscoelastic solids

A two-dimensional anisotropic elastic or viscoelastic solid indented by multiple rigid punches is considered. By taking the rigid body translation and rotation of each punch as the additional variables to the usual contact boundary element method (BEM), we propose a brand-new BEM in which the additional equations come from the force/moment equilibrium of each punch. In this newly developed BEM, the selected fundamental solutions are valid for the general anisotropic elastic/viscoelastic solids with or without holes/cracks. Under this consideration, no meshes are required on the boundaries of rigid punches and holes/cracks, which makes it much more accurate and efficient than the conventional contact BEM. This method is valid for the frictionless or frictional contact surface, and the punches can be in equilibrium status or in quasistatic sliding condition. If the solids are anisotropic elastic, it is applicable for both incomplete and complete indentation. Since the extension from elastic to viscoelastic is based upon the elastic-viscoelastic correspondence principle that requires all the boundaries be time-independent, our method is valid only for complete indentation if the indented solid is viscoelastic. In addition to this new BEM, in order to verify our results for the cases with viscoelastic solids, by proper use of Laplace transform and its inversion, new analytical solutions for the indentation by a flat-ended/parabolic punch are also presented for the half-plane made by anisotropic viscoelastic materials.