9. Isothermal Boundary-Value Problems

This chapter contains a comprehensive discussion of the types of boundary-value problems encountered in linear viscoelasticity. The chapter presents detailed solution methods for compressible and incompressible solids, including materials with synchronous moduli, whose property functions are assumed to have the same time dependence. The method of separation of variables in the time domain and frequency domains is also described in full, as is the use of the Laplace and Fourier transformations. The elastic–viscoelastic correspondence principle, which allows viscoelastic solutions to be constructed from equivalent elastic ones and as a consequence of the applicability of integral transforms, is also developed and examined in detail.