Mathematical and physical aspects of the solution to the Cauchy problem for a nonlocal model of viscoelasticity

Abstract The aim of this paper is to present a new system of equations describing a nonlocal model of viscoelasticity theory. In order to obtain the model we used a new approach to the constitutive relations for the internal energy and stress tensor. Using the modified Cagniard‐de Hoop method we constructed the fundamental solution to this system of equations in the three‐dimensional space. Basing on the derived fundamental solutions, explicit formulae for the solution to the Cauchy problem for this system of equations were presented. For the obtained solution, its mechanical and mathematical aspects and properties have been analyzed for the considered viscoelastic medium.