Static Deformations of Solids

Abstract

We now have enough machinery to begin to find solutions to problems involving the static deformation of elastic solids. In Chap. 7 we will discuss the dynamic behavior of solids. Most of our discussion will be restricted to the discussion of linear, isotropic solids, characterized by two material constants (we will mostly use the Young’s modulus E and Poisson’s ratio v, but one could just as well use the two Lamé constants λ and μ). Extensions to the treatment of general linear elastic solids, using the 6 × 6 stiffness matrix c or the compliance matrix s, are possible, but involve such intricate manipulations of complex differential equations that such problems are usually relegated to numerical solutions. We will illustrate some of the differences between isotropic and non-isotropic solids in the examples.