Mechanically concealed holes

Abstract

When a hole is introduced into an elastic material, it will usually act to reduce the overall mechanical stiffness. A general ambition is to investigate whether a stiff shell around the hole can act to maintain the overall mechanical properties. We consider this effect from a macroscopic continuum perspective down to atomistic scales. For this purpose, we focus on the basic continuum example situation of an isotropic, homogeneous, linearly elastic material loaded uniformly under compressive plane strain for low concentrations of holes. As we demonstrate, the thickness of the shell can be adjusted in a way to maintain the overall stiffness of the system. We derive a corresponding mathematical expression for the thickness of the shell that conceals the hole. Thus, one can work with given materials to mask the presence of the holes simply by adjusting the thickness of the surrounding shells, with no need to change the materials. Our predictions from linear elasticity continuum theory are extended to atomistic levels using molecular dynamics simulations of a model Lennard-Jones solid. These extensions attest the robustness of our predictions down to atomistic scales. Thus, they open a straightforward possibility to adjust the strategy of mechanical cloaking via atomistic manipulations. From both perspectives, the underlying concept is important in the context of light-weight construction.