Energy minimizing twinning with variable volume fraction, for two nonlinear elastic phases with a single rank-one connection

DOI10.1142/S0218202522500397zbMath1504.74067OpenAlexW4281382985MaRDI QIDQ5045192

Oleksandr Misiats, Robert V. Kohn, Sergio Conti

Publication date: 4 November 2022

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

Full work available at URL: https://doi.org/10.1142/s0218202522500397

zbMATH Keywords

upper boundnonlinear elasticitylower boundenergy scaling lawsolid-solid phase transitionvariable volume fraction twinning

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Existence of solutions for minimax problems (49J35) Analysis of microstructure in solids (74N15)

Related Items (1)

On scaling properties for two-state problems and for a singularly perturbed \(T_3\) structure

Cites Work

• Fine phase mixtures as minimizers of energy
• Energy Scaling and Domain Branching in Solid-Solid Phase Transitions
• Zig-zag twins and helical phase transformations
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• Surface energy and microstructure in coherent phase transitions
• Relaxation and regularization of nonconvex variational problems
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Energy scaling and branched microstructures in a model for shape-memory alloys with SO(2) invariance
• Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys
• Direct methods in the calculus of variations
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