• DOI:10.1137/20m1355823
• Corpus ID: 220546379

Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model

@article{Negri2021ExistenceEI,
  title={Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model},
  author={Matteo Negri and Riccardo Scala},
  journal={SIAM J. Math. Anal.},
  year={2021},
  volume={53},
  pages={5682-5730}
}

• M. Negri, Riccardo Scala
• Published 16 July 2020
• Mathematics
• SIAM J. Math. Anal.

We study the dynamics of visco-elastic materials coupled by a common cohesive interface (or, equivalently, {two single domains separated by} a prescribed cohesive crack) in the anti-plane setting. We consider a general class of traction-separation laws featuring an activation threshold on the normal stress, softening and elastic unloading. In strong form, the evolution is described by a system of PDEs coupling momentum balance (in the bulk) with transmission and Karush-Kuhn-Tucker conditions (on the interface). We provide a detailed analysis of the system. We first prove existence of a weak solution, employing a time discrete approach and a regularization of the initial data. Then, we prove our main results: the energy identity and the existence of { solutions} with acceleration in $L^\infty (0,T; L^2)$.