Stochastic homogenisation of free-discontinuity problems
In this paper we study the stochastic homogenisation of free-discontinuity functionals.
Assuming stationarity for the random volume and surface integrands, we prove the existence …
Assuming stationarity for the random volume and surface integrands, we prove the existence …
Gradient damage models for heterogeneous materials
In this paper we study the asymptotic behaviour of phase-field functionals of Ambrosio and
Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse …
Tortorelli type allowing for small-scale oscillations both in the volume and in the diffuse …
-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation
We analyze the $\Gamma $-convergence of sequences of free-discontinuity functionals
arising in the modeling of linear elastic solids with surface discontinuities, including …
arising in the modeling of linear elastic solids with surface discontinuities, including …
A compactness result in and applications to -convergence for free discontinuity problems
M Friedrich - Calculus of Variations and Partial Differential …, 2019 - Springer
We present a compactness result in the space GSBV^ p GSBV p which extends the classical
statement due to Ambrosio (Arch Ration Mech 111: 291–322, 1990) to problems without a …
statement due to Ambrosio (Arch Ration Mech 111: 291–322, 1990) to problems without a …
Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with
non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial …
non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial …
-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals
We study the limit behaviour of singularly-perturbed elliptic functionals of the form F k (u,
v)=∫ A v 2 fk (x,∇ u) dx+ 1 ε k∫ A gk (x, v, ε k∇ v) dx, where u is a vector-valued Sobolev …
v)=∫ A v 2 fk (x,∇ u) dx+ 1 ε k∫ A gk (x, v, ε k∇ v) dx, where u is a vector-valued Sobolev …
New homogenization results for convex integral functionals and their Euler–Lagrange equations
M Ruf, M Schäffner - Calculus of Variations and Partial Differential …, 2024 - Springer
We study stochastic homogenization for convex integral functionals u↦∫ DW (ω, x ε,∇ u)
dx, where u: D⊂ R d→ R m, defined on Sobolev spaces. Assuming only stochastic …
dx, where u: D⊂ R d→ R m, defined on Sobolev spaces. Assuming only stochastic …
[HTML][HTML] Discrete stochastic approximations of the Mumford–Shah functional
M Ruf - Annales de l'Institut Henri Poincaré C, Analyse non …, 2019 - Elsevier
We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional.
The discrete functionals act on functions defined on stationary stochastic lattices and take …
The discrete functionals act on functions defined on stationary stochastic lattices and take …
Functionals Defined on Piecewise Rigid Functions: Integral Representation and -Convergence
We analyse integral representation and\varGamma Γ-convergence properties of functionals
defined on piecewise rigid functions, that is, functions which are piecewise affine on a …
defined on piecewise rigid functions, that is, functions which are piecewise affine on a …
Stochastic homogenization of degenerate integral functionals and their Euler-Lagrange equations
M Ruf, T Ruf - arxiv preprint arxiv:2109.13013, 2021 - arxiv.org
We prove stochastic homogenization for integral functionals defined on Sobolev spaces,
where the stationary, ergodic integrand satisfies a degenerate growth condition of the …
where the stationary, ergodic integrand satisfies a degenerate growth condition of the …