9 papers · 1 filter
Solid-solid phase transitions with space-dependent wells
Elisa Davoli, Jakob Deutsch, Manuel Friedrich +1
We investigate a second-order Modica-Mortola functional of the form \[ E_\varepsilon[u] := \int_Ω\frac{1}{\varepsilon} W(x, \nabla u) + \varepsilon|\nabla^2 u|^2 \, dx, \] which mo…
Quasistatic evolution of cohesive-type fracture
Vito Crismale, Manuel Friedrich
We prove the existence of globally stable quasistatic evolutions for a cohesive fracture model with unprescribed crack path and without any topological restriction, in arbitrary di…
Eigenfracture approximation of quasi-static crack growth in brittle materials
Ba Duc Duong, Manuel Friedrich
We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending o…
Hausdorff dimension of the singular set for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We consider regularity of the crack set associated to a minimizer of the Griffith fracture energy, often used in modeling brittle materials. We show that the crack is uniformly rec…
Adaptive finite element approximation for quasi-static crack growth
Vito Crismale, Manuel Friedrich, Joscha Seutter
We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are define…
Linearization of quasistatic fracture evolution in brittle materials
Manuel Friedrich, Pascal Steinke, Kerrek Stinson
We prove a linearization result for quasistatic fracture evolution in nonlinear elasticity. As the stiffness of the material tends to infinity, we show that rescaled displacement f…
Strong existence for free discontinuity problems in linear elasticity
Manuel Friedrich, Camille Labourie, Kerrek Stinson
In this note we show Ahlfors-regularity for a large class of quasiminimizers of the Griffith functional. This allows us to prove that, for a range of free discontinuity problems in…
Atomistic-to-continuum convergence for quasi-static crack growth in brittle materials
Manuel Friedrich, Joscha Seutter
We study the atomistic-to-continuum limit for a model of a quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spri…
An epsilon-regularity result for Griffith almost-minimizers in the plane
Manuel Friedrich, Camille Labourie, Kerrek Stinson
We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we…