Kink-type solitary waves within the quasi-linear viscoelastic model

The quasi-linear model of viscoelasticity is a constitutive law widely used to investigate the time dependent behaviour of soft tissues and bio-materials. For this model, we study the shearing motion and discuss the existence of kink-type wave solutions. In particular, we derive a nonlinear second-order ordinary differential equation which allows to widen the class of solutions given by Samsonov (1995). When the stress relaxation function is a Prony series, kink-wave solutions can exist for strongly elliptic strain energy functions, except for the Mooney-Rivlin model. We provide numerical simulations for the Yeoh model. (C) 2018 Elsevier B.V. All rights reserved.