Calculus of Variations and Geometric Measure Theory

M. Caponi - F. Sapio

A dynamic model for viscoelastic materials with prescribed growing cracks

created by sapio on 30 Apr 2019
modified by caponi on 06 Nov 2023


Published Paper

Inserted: 30 apr 2019
Last Updated: 6 nov 2023

Journal: Annali di Matematica Pura ed Applicata (1923 -)
Volume: 199
Pages: 1263-1292
Year: 2020
Doi: 10.1007/s10231-019-00921-1

ArXiv: 1904.13104 PDF
Links: Journal site


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.

Keywords: elastodynamics, Viscoelasticity, linear second order hyperbolic systems, dynamic fracture mechanics, cracking domains