Deformations and motions in compressible non-linear elasticity

Abstract

The primary purpose of this study is to identify solutions for deformations and motions in compressible non-linear elasticity. The research study mainly focuses on the mathematical theory of deformations and motions of non-linearly elastic compressible hollow spheres and hollow cylinders reinforced with inextensible fibers in the radial direction. Static and dynamic solutions for both unstressed and everted cases are presented for the hollow spheres and hollow cylinders of isotropic elastic materials that are radially inextensible. Different strain energy density functions are then applied for further demonstration to the extent allowed by the analytical approach. This thesis is concerned with the mathematical theory of non-linear elasticity and no discussion of shell or membrane theories, or of numerical methods is included. The setting is purely isothermal and no reference is made to thermodynamics. Attention is confined to twice-continuously differentiable deformations; discontinuities are not considered.