Laminated microstructure in a variational problem with a non-rank-one connected double well potential

DOI10.1006/jmaa.1997.5722zbMath0945.49010OpenAlexW2034530721MaRDI QIDQ1378636

Zhiping Li

Publication date: 27 July 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5722

zbMATH Keywords

variational problemconforming finite element methodlaminated microstructurenon-rank-one connected double well potential

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (6)

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 ⋮ Computations of needle-like microstructures ⋮ A regularized mesh transformation method for the computation of crystalline microstructures

Cites Work

• Numerical analysis of oscillations in nonconvex problems
• Fine phase mixtures as minimizers of energy
• Simultaneous numerical approximation of microstructures and relaxed minimizers
• Optimal-Order Error Estimates for the Finite Element Approximation of the Solution of a Nonconvex Variational Problem
• Numerical Analysis of a Nonconvex Variational Problem Related to Solid-Solid Phase Transitions
• Numerical solution of the scalar double-well problem allowing microstructure
• Existence of minimizers and microstructure in nonlinear elasticity
• Numerical Approximation of the Solution of a Variational Problem with a Double Well Potential
• Direct methods in the calculus of variations
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