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Kink-type solitary waves within the quasi-linear viscoelastic model. (English) Zbl 07215428
Summary: 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 A. M. Samsonov [Appl. Anal. 57, No. 1–2, 85–100 (1995; Zbl 0879.35111)]. 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.

MSC:
35 Partial differential equations
74 Mechanics of deformable solids
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