Boltzmann hereditary integral

The elastic-viscoelastic correspondence says that the viscoelastic solution can be generated from the elastic one using a Boltzmann hereditary integral (hereditary for past dependent) with respect to past time from f = 0 to the present time if = t. This is illustrated as... 

The general approach to discussing linear viscoelasticity comes from the Boltzmann superposition principle represented as a hereditary integral. For the shear stress as a function of shear strain, one obtains... 

The viscoelastic response is commonly described by using a form of Boltzmann "s hereditary integral, referred to as the excitation-response theory (Gurtin and Sternberg 1962 Yamamoto 1972 Christensen 2003). 

Using the elastic-viscoelastic correspondence with hereditary Boltzmann Integral allows for the general solution to be found as (Section 6.4.5.S, Shimizu, Yanagimoto, and Sakai, 1999 Sakai, 2002 Fischer-Cripps, 2004b Cheng and Cheng, 2005 Oyen, 2005 Bernard et ai, 2010)... 

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