Ten remarks on nonconvex minimisation for phase transition simulations

DOI10.1016/j.cma.2004.05.012zbMath1143.74348OpenAlexW2130329569MaRDI QIDQ1777101

Carsten Carstensen

Publication date: 12 May 2005

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2004.05.012

zbMATH Keywords

Adaptive algorithmPhase transitionStrong convergenceComputational microstructureNonconvex minimisationRelaxation theory

Mathematics Subject Classification ID

Related Items (7)

Simulation of phase combinations in shape memory alloys patches by hybrid optimization methods ⋮ The method of moments for some one-dimensional, non-local, non-convex variational problems ⋮ Coarse-Convex-Compactification Approach to Numerical Solution of Nonconvex Variational Problems ⋮ Using discrete optimization algorithms to find minimum energy configurations of slender cantilever beams with non-convex energy functions ⋮ Computational Microstructures in Phase Transition Solids and Finite-Strain Elastoplasticity ⋮ Theory and finite element computations of a unified cyclic phase transformation model for monocrystalline materials at small strains ⋮ Error Analysis of a Dual-parametric Bi-quadratic FEM in Cavitation Computation in Elasticity

Cites Work

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• Averaging techniques yield reliable a posteriori finite element error control for obstacle problems
• Fine phase mixtures as minimizers of energy
• The relaxation of a double-well energy
• Convexity conditions and existence theorems in nonlinear elasticity
• On the non-locality of quasiconvexity
• The computation of the dynamics of the martensitic transformation
• Averaging techniques for reliable a posteriori FE error control in elastoplasticity with hardening
• Adaptive finite element methods for microstructures? Numerical experiments for a 2-well benchmark
• Energetic formulation of multiplicative elasto-plasticity using dissipation distances
• Multiscale resolution in the computation of crystalline microstructure
• An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads
• Quasistatic crack growth in nonlinear elasticity
• Variational methods for crystalline microstructure. Analysis and computation
• Convergent adaptive finite elements for the nonlinear Laplacian
• Convergence for stabilisation of degenerately convex minimisation problems
• Adaptive finite element methods with convergence rates
• Nonconvex energy minimization and dislocation structures in ductile single crystals
• Effective relaxation for microstructure simulations: algorithms and applications
• Quasi-convexity and the lower semicontinuity of multiple integrals
• Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids
• Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations
• Rank-one convexity does not imply quasiconvexity
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
• Strong Convergence of Numerical Solutions to Degenerate Variational Problems
• Implicit Time Discretization and Global Existence for a Quasi-Linear Evolution Equation with Nonconvex Energy
• Numerical solution of the scalar double-well problem allowing microstructure
• Numerical Methods for a Nonconvex Optimization Problem Modeling Martensitic Microstructure
• Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis
• Numerical Analysis of Compatible Phase Transitions in Elastic Solids
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
• Non–convex potentials and microstructures in finite–strain plasticity
• Time-Space Discretization of the Nonlinear Hyperbolic Systemu_tt= div (\sigma(Du)+Du_t)
• Local Stress Regularity in Scalar Nonconvex Variational Problems
• Convergence of Adaptive Finite Element Methods
• Local problems on stars: A posteriori error estimators, convergence, and performance
• All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable
• On the planar rank-one convexity condition
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Reliable and Efficient Approximation of Polyconvex Envelopes
• Direct methods in the calculus of variations
• Averaging technique for a posteriori error control in elasticity. III: Locking-free nonconforming FEM.

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