A dynamic model for viscoelastic materials with prescribed growing cracks

Abstract

In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy--dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

References in corpus (1)

• Existence and uniqueness of dynamic evolutions for a one-dimensional debonding model with damping

Cited by in corpus (4)

• A dynamic model for viscoelasticity in domains with time-dependent cracks
• An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains
• Nonlinear dynamic fracture problems with polynomial and strain-limiting constitutive relations
• The viscoelastic paradox in a nonlinear Kelvin-Voigt type model of dynamic fracture