12. Viscoelastic Materials

Viscoelastic materials exhibit a time and rate dependence that is completely absent in the elastic materials. To understand the mechanical behavior of viscoelastic materials, solutions for the deformations and stresses are generally required. Through the use of correspondence principle between linear elasticity and linear viscoelasticity, the Stroh formalism for linear anisotropic viscoelasticity will be introduced in this chapter. With this formalism, the viscoelastic solids can be treated effectively in Laplace domain and the solutions in time domain can be obtained by numerical inversion of the Laplace transform. Solutions for the related viscoelastic problems of holes, cracks, inclusions, interface corners, and contact (only for complete indentation) discussed previously for anisotropic elastic materials, will then be presented in this chapter. Although the elastic-viscoelastic correspondence principle is simple and directly related to its corresponding elastic system, it can only be applied to the cases with time-invariant boundaries. To solve the general problems of anisotropic viscoelasticity, an alternative approach called time-stepping method will be introduced later in Sect. 15.8.3. By that approach, the problems with time-dependent boundaries can also be solved through their associated solutions of elasticity.