preprint
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Inserted: 13 nov 2026
Last Updated: 13 nov 2026

Year: 2026

Abstract:

For a variational model of incompressible elastomers exhibiting cavitation, we establish the existence of irreversible quasi-static evolutions driven by time-dependent boundary conditions. Our result extends previous work by Mora-Corral (2014) to incompressible materials under weaker regularity assumptions on the boundary datum. The proof employs the multiplicative splitting introduced by Francfort and Mielke (2006) to reduce the problem to time-independent boundary conditions and then invokes abstract results on the existence of energetic solutions to rate-independent systems. Specifically, the construction of mutual recovery sequences requires particular attention to accommodate the incompressibility constraint: to this end we employ the method by Moser (1965) to exhibit incompressible diffeomorphisms interpolating between localized translations and the identity.