A new fractional viscoelastic model for an infinitely thermoelastic body with a spherical cavity including Caputo-Fabrizio operator without singular kernel

Abstract

Many applications and contexts including materials science, metallurgy, and solid-state physics, are concerned with the study of the behavior of viscoelastic materials. In addition, any composite or complex construction containing embedded polymers exhibits viscoelastic behavior under static and dynamic stress conditions. Wide types of linear/nonlinear constitutive models have been proposed to define the viscoelastic deformation process of viscoelastic materials in order to explore their mechanical behavior. However, it has been shown that the constitutive relationship in the integer-order of stress-strain available in conventional viscoelastic models may fail in some types of situations and do not match well with empirical evidence. In this paper, a novel mathematical model is provided that uses Caputo-Fabrizio fractional-order derivatives to describe the viscoelastic phenomena and is consistent with thermodynamic principles. The Caputo-Fabrizio kernel has many features, such as nonlocality and non-singularity in addition to the exponential form. The suggested model is used to study the dynamic reactions of an unbounded body with a spherical cavity made of viscoelastic material subjected to time-varying heat. Using the Laplace transform technique, numerical calculations of many physical fields are obtained and explored in depth.