Linear Viscoelastic Boundary Value Problems

In most published works on viscoelastic stress analysis the constitutive equations of the materials are expressed in linear differential operator forms. However, due to the mathematical complexity which arises when a realistic number of terms are used to properly characterize the material, these analyses have generally been limited to either short time intervals or unrealistic material representations. To overcome this difficulty, a more general method of representation for the constitutive equations of linear viscoelastic materials is achieved through the use of the hereditary integrals. Use of such constitutive equations permits an easy formulation of the time dependent expressions in the form of integral equations involving multiple convolution integrals which involve all the time dependent variables. The evaluation of these convolution integrals and the numerical solution of the integral equations then provides the response of the materials over broad time intervals. The general applicability of this method and practical techniques for its execution are discussed.