Hereditary Integral Representations of Stress and Strain

Abstract

As discussed previously, the relation between stress and strain for linear viscoelastic materials involves time and higher derivatives of both stress and strain. While the differential equation method can be quite general, a hereditary integral method has proved to be appealing in many situations. This hereditary integral equation approach is attributed to Boltzman and was only one of his many accomplishments. In the late nineteenth century, when the method was first introduced, considerable controversy arose over the procedure. Now, it is the method of choice for the mathematical expression of viscoelastic constitutive (stress-strain) equations. For an excellent discussion of these efforts of Boltzman, see Markovitz (1977).