A dynamic model for viscoelastic materials with prescribed growing cracks
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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.
KeywordsLinear second-order hyperbolic systems Dynamic fracture mechanics Elastodynamics Viscoelasticity Cracking domains
Mathematics Subject Classification35L53 35A01 35Q74 74H20 74R10 74D05
The authors wish to thank Professors Gianni Dal Maso and Rodica Toader for having proposed the problem and for many helpful discussions on the topic. The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).
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