A dynamic model for viscoelastic materials with prescribed growing cracks

  • Maicol CaponiEmail author
  • Francesco Sapio


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.


Linear second-order hyperbolic systems Dynamic fracture mechanics Elastodynamics Viscoelasticity Cracking domains 

Mathematics Subject Classification

35L53 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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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.SISSATriesteItaly

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