Some inhomogeneous motions and deformations within the context of a non-linear elastic solid

Abstract

We study inhomogeneous shearing deformations and motions of slabs and solid cylinders of generalized neo-Hookean solids. We find that solutions which have a boundary layer structure are possible, in that the deformation is highly inhomogeneous near the boundary and essentially homogeneous in a core region. We also study the inhomogeneous twisting of a slab of a generalized neo-Hookean material about distinct axes, allowing for discontinuous deformation gradients. For certain values of parameters, we find that the equations admit solutions for which the locus of the centers of rotation is piecewise continuously differentiable.