Stress-rate-type strain-limiting models for solids resulting from implicit constitutive theory

Abstract

The main objective of this work is two-fold. First, we investigate the stress-rate-type implicit constitutive relations for solids within the context of strain-limiting theory of material response. The relations we study are models for generalisations of elastic bodies whose strain depends on the stress and the stress rate. Secondly, we obtain travelling-wave solutions for some special cases that are nonlinear in the stress. These are the first notion of solutions available in the literature for this type of models describing stress-rate-type materials.

Existence of solutions for stress-rate type strain-limiting viscoelasticity in Gevrey spaces

“…Note that we use the shorthand hfalse(Tfalse) for hfalse(Tfalse(⋅,⋅false)false). A detailed derivation of this model can be found in [6,7]. Since the constitutive relation also depends on the stress-rate Tt, the model is also referred to as a stress-rate type model.…”

“…Duman & Şengül [6] proved the existence of travelling wave solutions for a related case of this partial differential equation (PDE) on R×false[0,normal∞false). They considered an equation with the second term in (1.1) being equal to false(γfalse(Tfalse)Ttfalse)tt with γfalse(⋅false) being a function of the stress satisfying certain assumptions.…”