We consider a system of one-dimensional elastic and brittle media coupled by an elastic term. Both the coupling and the fracture-energy coefficient depend on a small parameter ɛ . We describe the quasistatic motion of this system under varying boundary conditions at ɛ fixed, interpreting the fracture energy term as a dissipation as in the variational approach to fracture growth, by analysing a time-discrete approximation. The motion is characterized by the onset of successive fracture sites. We study the behaviour of these evolutions with vanishing dissipations as ɛ , characterizing the possible limit of the energies by a one-parameter family of time-parameterized functions. We show that, after an initial time interval, a function in this family corresponds to a minimum of the -limit of the energies of the system only for a discrete set of the values of the quantity parameterizing boundary conditions.

A singular limit of a family of variational evolutions for a brittle elastic bi-layer / Causin, A.; Solci, M.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 112949:(In corso di stampa), pp. 1-20. [10.1016/j.na.2022.112949]

A singular limit of a family of variational evolutions for a brittle elastic bi-layer

Causin, A.;Solci, M.
In corso di stampa

Abstract

We consider a system of one-dimensional elastic and brittle media coupled by an elastic term. Both the coupling and the fracture-energy coefficient depend on a small parameter ɛ . We describe the quasistatic motion of this system under varying boundary conditions at ɛ fixed, interpreting the fracture energy term as a dissipation as in the variational approach to fracture growth, by analysing a time-discrete approximation. The motion is characterized by the onset of successive fracture sites. We study the behaviour of these evolutions with vanishing dissipations as ɛ , characterizing the possible limit of the energies by a one-parameter family of time-parameterized functions. We show that, after an initial time interval, a function in this family corresponds to a minimum of the -limit of the energies of the system only for a discrete set of the values of the quantity parameterizing boundary conditions.
A singular limit of a family of variational evolutions for a brittle elastic bi-layer / Causin, A.; Solci, M.. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 112949:(In corso di stampa), pp. 1-20. [10.1016/j.na.2022.112949]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/299044
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact