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Homogenization of Griffith's Criterion for brittle Laminates
Matteo Negri
We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evo…
Existence, energy identity and higher time regularity of solutions to a dynamic visco-elastic cohesive interface model
Matteo Negri, Riccardo Scala
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 ant…
A quasi-static model for craquelure patterns
Matteo Negri
We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the qua…
Weak solutions for gradient flows under monotonicity constraints
Matteo Negri, Masato Kimura
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solut…
Analysis of staggered evolutions for nonlinear energies in phase field fracture
Stefano Almi, Matteo Negri
We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. We analyze the time-d…