ABSTRACT
This chapter considers problems of determining stress, strain, or displacement fields in viscoelastic bodies. It generalizes the constitutive equations from one dimension to three dimensions. The chapter solves a problem in simple beam theory for a viscoelastic material, illustrating the approach of direct construction. It is simpler in this case to use the correspondence principle which simplifies solution for certain boundary value problems in viscoelastic materials. As input to the correspondence principle one uses a corresponding solution for an elastic material. The chapter develops several examples involving use of the correspondence principle. It examines problems not amenable to the correspondence principle. As the governing equations are carried through to obtain a solution, the distinction between the elastic and viscoelastic cases in the Laplace domain consists of merely the extra factors of s, which then appear in the final solution.
