The regularisation of theN-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions
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Publication:3628299
DOI10.1051/cocv:2008039zbMath1161.74044OpenAlexW2155750499MaRDI QIDQ3628299
Publication date: 19 May 2009
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/245484
surface energynon-convex variational problemquasiconvex hullcrystalline microstructurestored energy density function
Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Finite element methods applied to problems in solid mechanics (74S05) Energy minimization in equilibrium problems in solid mechanics (74G65) Analysis of microstructure in solids (74N15)
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On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation ⋮ A compactness and structure result for a discrete multi-well problem with \(\mathrm{SO}(n)\) symmetry in arbitrary dimension ⋮ A Two Well Liouville Theorem ⋮ Convex integration solutions for the geometrically nonlinear two-well problem with higher Sobolev regularity
Cites Work
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- The Euler equations as a differential inclusion
- Fine phase mixtures as minimizers of energy
- Equilibrium configurations of crystals
- Singular perturbations as a selection criterion for periodic minimizing sequences
- Fine properties of functions with bounded deformation
- General existence theorems for Hamilton-Jacobi equations in the scalar and vectorial cases
- Liquid-like behavior of shape memory alloys.
- Convex integration for Lipschitz mappings and counterexamples to regularity
- A new approach to counterexamples to \(L^1\) estimates: Korn's inequality, geometric rigidity, and regularity for gradients of separately convex functions
- The appearance of microstructures in problems with incompatible wells and their numerical approach
- Microstructures with finite surface energy: The two-well problem
- Convex integration with constraints and applications to phase transitions and partial differential equations
- Relaxed constitutive relations for phase transforming materials
- Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions
- Parabolic systems with nowhere smooth solutions
- Deformations with finitely many gradients and stability of quasiconvex hulls
- An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure
- Proposed experimental tests of a theory of fine microstructure and the two-well problem
- Surface energy and microstructure in coherent phase transitions
- A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
- Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance
- Optimal existence theorems for nonhomogeneous differential inclusions
- Comparing two methods of resolving homogeneous differential inclusions
