Elastic and inelastic material behaviour

Abstract

Introduction Geotechnical engineers have made good use of the theory of elasticity for a number of decades. It became clear near the end of the nineteenth century that a variety of problems involving an elastic halfspace could be solved using techniques developed by the French mathematician Joseph Boussinesq. Boussinesq solved the problem of a point load resting on the surface of a homogeneous isotropic linearly elastic halfspace. He also developed the solution for a rigid circular footing resting on the halfspace surface. His work inspired others to investigate related problems with the result that by the middle of the twentieth century a wide range of problems involving both homogeneous and layered halfspaces with isotropic and anisotropic elastic materials had been solved for a variety of loading conditions. Solutions continue to appear in the geotechnical literature as well as in other disciplines. There are also coupled solutions in which porous materials saturated with pore fluid are modelled incorporating both elastic deformation and pore fluid flow. In this chapter we will outline the basic elements of behaviour of elastic materials. The stress–strain relations for isotropic materials are given in a variety of forms and relationships between the elastic constants are derived. We will note the bounds imposed on the elastic constants by thermodynamic requirements and we discuss some special classes of problems such as plane strain problems and problems involving incompressible materials. Much of this material is also presented in EG , often in more detail.