Existence results for a class of rate-independent material models with nonconvex elastic energies
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Publication:5479403
DOI10.1515/CRELLE.2006.044zbMath1101.74015WikidataQ59901965 ScholiaQ59901965MaRDI QIDQ5479403
Gilles A. Francfort, Alexander Mielke
Publication date: 7 July 2006
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Theories of fracture and damage (74A45) Existence of solutions of dynamical problems in solid mechanics (74H20)
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Cites Work
- Using the gradients of temperature and internal parameters in continuum thermodynamics
- Damage, gradient of damage and principle of virtual power
- A density result in two-dimensional linearized elasticity, and applications
- Energetic formulation of multiplicative elasto-plasticity using dissipation distances
- A model for the quasi-static growth of brittle fractures: Existence and approximation results
- A variational formulation of rate-independent phase transformations using an extremum principle
- Existence results for energetic models for rate-independent systems
- Quasistatic crack growth in nonlinear elasticity
- Regularity of quasiconvex envelopes
- Nonconvex energy minimization and dislocation structures in ductile single crystals
- A variational formulation for nonlocal damage models
- Revisiting brittle fracture as an energy minimization problem
- Deriving new evolution equations for microstructures via relaxation of variational incremental problems
- Effective relaxation for microstructure simulations: algorithms and applications
- Existence and convergence for quasi-static evolution in brittle fracture
- A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys
- Non–convex potentials and microstructures in finite–strain plasticity
- Existence of Minimizers in Incremental Elasto-Plasticity with Finite Strains
- Local Stress Regularity in Scalar Nonconvex Variational Problems
- Semicontinuity problems in the calculus of variations
