A comparison of classical and new finite element methods for the computation of laminate microstructure

DOI10.1016/S0168-9274(99)00146-4zbMath1010.74063MaRDI QIDQ5928459

Matthias K. Gobbert, Andreas Prohl

Publication date: 13 May 2003

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

Young measuresdiscontinuous finite elementelastic energy minimizationequilibria of martensitic crystalsEricksen-James energygeometrically nonlinear continuum theorylaminate microstructureminimizing sequencesmulti-well problemnonconvex functionalsnonlinear conjugate gradientsnonlinear elasticity

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Crystalline structure (74E15) Finite element methods applied to problems in solid mechanics (74S05) Energy minimization in equilibrium problems in solid mechanics (74G65)

Related Items (5)

Numerical analysis and computation of a multi-order laminated microstructure ⋮ An averaging scheme for macroscopic numerical simulation of nonconvex minimization problems ⋮ Computation of the lower semicontinuous envelope of integral functionals and non-homogeneous microstructures ⋮ MULTISCALE MODELLING AND COMPUTATION OF MICROSTRUCTURES IN MULTI-WELL PROBLEMS ⋮ A regularized mesh transformation method for the computation of crystalline microstructures

Cites Work

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• Fine phase mixtures as minimizers of energy
• The computation of the dynamics of the martensitic transformation
• Parametrized measures and variational principles
• Approximation of a laminated microstructure for a rotationally invariant, double well energy density
• Adaptive algorithms for scalar non-convex variational problems
• Numerical analysis of oscillations in multiple well problems
• An approach to nonlinear programming
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• Numerical Approach to Double Well Problems
• Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions
• Strong Convergence of Numerical Solutions to Degenerate Variational Problems
• Numerical solution of the scalar double-well problem allowing microstructure
• Numerical Methods for a Nonconvex Optimization Problem Modeling Martensitic Microstructure
• Finite Element Analysis of Microstructure for the Cubic to Tetragonal Transformation
• Nonconforming finite element approximation of crystalline microstructure
• On Algorithms for Nonconvex Optimization in the Calculus of Variations
• A Discontinuous Finite Element Method for Solving a Multiwell Problem
• Direct methods in the calculus of variations

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