Energy Scaling and Domain Branching in Solid-Solid Phase Transitions

DOI10.1007/978-3-319-00786-1_11zbMath1326.35373OpenAlexW200606475MaRDI QIDQ2950231

Allan Chan, Sergio Conti

Publication date: 8 October 2015

Published in: Singular Phenomena and Scaling in Mathematical Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-00786-1_11

zbMATH Keywords

solid-solid phase transitions

Mathematics Subject Classification ID

Existence of solutions for minimax problems (49J35) Nonlinear constitutive equations for materials with memory (74D10) PDEs in connection with mechanics of deformable solids (35Q74)

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Cites Work

• Unnamed Item
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• Fine phase mixtures as minimizers of energy
• Energy minimization and flux domain structure in the intermediate state of a type-I superconductor
• Energy scaling of compressed elastic films -- three-dimensional elasticity and reduced theories
• Microstructures with finite surface energy: The two-well problem
• Convex integration with constraints and applications to phase transitions and partial differential equations
• Existence of Lipschitz minimizers for the three-well problem in solid-solid phase transitions
• A lower bound for a variational model for pattern formation in shape-memory alloys
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• Surface energy and microstructure in coherent phase transitions
• Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor
• Rigourous bounds for the Föppl-von Kármán theory of isotropically compressed plates