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:(2022), pp. 1-20. [10.1016/j.na.2022.112949]