Gradient Damage Models for Heterogeneous Materials
DOI10.1137/22m1499145zbMath1527.49010arXiv2205.13966MaRDI QIDQ6137591
Teresa Esposito, Roberta Marziani, Caterina Ida Zeppieri, Annika Bach
Publication date: 4 September 2023
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2205.13966
homogenization\(\Gamma\)-convergenceelliptic approximationgradient-damage modelfree-discontinuity functionalsphase-field functionals
Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05)
Related Items (2)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The variational approach to damage. II: The gradient damage models
- Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy
- Functional analysis, Sobolev spaces and partial differential equations
- Homogenization of nonconvex integral functionals and cellular elastic materials
- Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
- Integral representation on \(BV(\Omega )\) of \(\Gamma\)-limits of variational integrals
- An introduction to \(\Gamma\)-convergence
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- A density result in \(GSBD^p\) with applications to the approximation of brittle fracture energies
- Quasistatic crack growth in nonlinear elasticity
- Fracture models as \(\Gamma\)-limits of damage models
- Interaction between oscillations and singular perturbations in a one-dimensional phase-field model
- A homogenization result in the gradient theory of phase transitions
- Homogenization of free discontinuity problems
- \(\Gamma\)-convergence of free-discontinuity problems
- Surface tension and \(\Gamma\)-convergence of Van der Waals-Cahn-Hilliard phase transitions in stationary ergodic media
- Asymptotic Analysis of Ambrosio--Tortorelli Energies in Linearized Elasticity
- Approximation of functional depending on jumps by elliptic functional via t-convergence
- Gradient theory of phase transitions in composite media
- ON THE VARIATIONAL APPROXIMATION OF FREE-DISCONTINUITY PROBLEMS IN THE VECTORIAL CASE
- Fracture and plastic models as Γ-limits of damage models under different regimes
- HOMOGENIZATION OF ENERGIES DEFINED ON PAIRS SET-FUNCTION
- A relaxation result for energies defined on pairs set-function and applications
- Convex Analysis
- \(\Gamma\)-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals
- Γ-convergence and stochastic homogenisation of phase-transition functionals
This page was built for publication: Gradient Damage Models for Heterogeneous Materials
