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Shape optimization of light structures with general Hooke's laws
Dimitrios Andreakis, Flaviana Iurlano, Filip Rindler
For the minimum-compliance shape optimization problem it was established recently [\textit{Duke Math.\ J.} 172 (2023), 43--103] that a sequence of approximately optimal shapes of e…
Transition from Continuous to Jumping Solutions in 2D Quasi-static Elastic Contact Problems with Coulomb Friction: the Mathematics Underlying the Onset of Brake Squeal
Patrick Ballard, Flaviana Iurlano
We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting id…
Superlinear free-discontinuity models: relaxation and phase-field approximation
Sergio Conti, Matteo Focardi, Flaviana Iurlano
In this paper we develop the Direct Method in the Calculus of Variations for free-discontinuity energies whose bulk and surface densities exhibit superlinear growth, respectively f…
Piecewise rank-one approximation of vector fields with measure derivatives
Jean-Francois Babadjian, Flaviana Iurlano
This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with res…
Approximation of functions with possibly infinite jump set
Sergio Conti, Matteo Focardi, Flaviana Iurlano
We prove an approximation result for functions such that is -integrable, , and is integrable over the jump set…
Convergence of critical points for a phase-field approximation of 1D cohesive fracture energies
Marco Bonacini, Flaviana Iurlano
Variational models for cohesive fracture are based on the idea that the fracture energy is released gradually as the crack opening grows. Recently, [Conti, Focardi, and Iurlano, An…