Quasistatic evolution of a brittle thin film
From MaRDI portal
Publication:2492661
DOI10.1007/s00526-005-0369-yzbMath1089.74037arXivmath/0604557OpenAlexW2119063844MaRDI QIDQ2492661
Publication date: 14 June 2006
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0604557
Brittle fracture (74R10) Energy minimization in equilibrium problems in solid mechanics (74G65) Thin films (74K35) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)
Related Items (15)
Brittle fracture in linearly elastic plates ⋮ The mathematics of thin structures ⋮ Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation ⋮ A continuum model for brittle nanowires derived from an atomistic description by \(\Gamma \)-convergence ⋮ A Blake-Zisserman-Kirchhoff theory for plates with soft inclusions ⋮ Brittle membranes in finite elasticity ⋮ A variational model for fracture and debonding of thin films under in-plane loadings ⋮ New results on \(\varGamma\)-limits of integral functionals ⋮ A quasistatic evolution model for perfectly plastic plates derived by \(\varGamma\)-convergence ⋮ A dimension-reduction model for brittle fractures on thin shells with mesh adaptivity ⋮ A quasistatic evolution model for the interaction between fracture and damage ⋮ Dimensional reduction for energies with linear growth involving the bending moment ⋮ A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics ⋮ Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity ⋮ Quasistatic evolution of magnetoelastic plates via dimension reduction
Cites Work
- Unnamed Item
- Unnamed Item
- Existence theory for a new class of variational problems
- An introduction to \(\Gamma\)-convergence
- An asymptotic study of the debonding of thin films
- Integral representation results for functionals defined on \(\text{SBV}(\Omega;\mathbb{R}^ m)\)
- A global method for relaxation in \(W^{1,p}\) and in SBV\(_p\)
- Ambrosio-Tortorelli approximation of quasi-static evolution of brittle fractures
- Quasistatic crack growth in nonlinear elasticity
- Regularity of quasiconvex envelopes
- Relaxation in \(BV\) versus quasiconvexification in \(W^{1,p}\); a model for the interaction between fracture and damage
- The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity
- Revisiting brittle fracture as an energy minimization problem
- Homogenization of free discontinuity problems
- A \(\Gamma\)-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications
- 3D-2D Asymptotic Analysis for Inhomogeneous Thin Films
- Existence and convergence for quasi-static evolution in brittle fracture
- Direct methods in the calculus of variations
- Brittle thin films
This page was built for publication: Quasistatic evolution of a brittle thin film
