Relaxation of a model energy for the cubic to tetragonal phase transformation in two dimensions

DOI10.1142/S0218202514500419zbMath1304.49027arXiv1403.4877OpenAlexW2964064349WikidataQ59965867 ScholiaQ59965867MaRDI QIDQ2932526

Georg Dolzmann, Sergio Conti

Publication date: 1 December 2014

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.4877

zbMATH Keywords

variational problemquasiconvexityrelaxationnonlinear elasticitycubic-to-tetragonal phase transformation

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45)

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Cites Work

• Unnamed Item
• Quasiconvex functions incorporating volumetric constraints are rank-one convex
• Constitutive theory for some constrained elastic crystals
• Fine phase mixtures as minimizers of energy
• Equilibrium configurations of crystals
• Self-accommodation in martensite
• The relaxation of a double-well energy
• Macroscopic response of nematic elastomers via relaxation of a class of \(SO(3)\)-invariant energies
• Liquid-like behavior of shape memory alloys.
• Variational methods for crystalline microstructure. Analysis and computation
• The two-well problem in three dimensions
• Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions
• Single-slip elastoplastic microstructures
• Ideally soft nematic elastomers
• RELAXATION OF A MODEL IN FINITE PLASTICITY WITH TWO SLIP SYSTEMS
• Asymptotic Behavior of Crystal Plasticity with One Slip System in the Limit of Rigid Elasticity
• Optimal design and relaxation of variational problems, II
• ELASTIC MATERIALS WITH TWO PREFERRED STATES
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• Numerical solution of the scalar double-well problem allowing microstructure
• Infinite-order laminates in a model in crystal plasticity

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