Quantitative Aspects of the Rigidity of Branching Microstructures in Shape Memory Alloys via H-Measures

DOI10.1137/18M1220017zbMath1480.74244arXiv1801.01338OpenAlexW3188346389MaRDI QIDQ4958011

Theresa M. Simon

Publication date: 6 September 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1801.01338

zbMATH Keywords

calculus of variationslinearized elasticityshape memory alloygamma convergenceH-measurecubic-to-tetragonal transformationHausdorff fractional dimension

Mathematics Subject Classification ID

Analysis of microstructure in solids (74N15) Equations linearized about a deformed state (small deformations superposed on large) (74B15) Bounds for solutions of equilibrium problems in solid mechanics (74G45)

Related Items (4)

On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation ⋮ On the energy scaling behaviour of singular perturbation models with prescribed dirichlet data involving higher order laminates ⋮ Energy scaling laws for microstructures: from helimagnets to martensites ⋮ Asymptotic self-similarity of minimizers and local bounds in a model of shape-memory alloys

Cites Work

• Fine phase mixtures as minimizers of energy
• The relaxation of a double-well energy
• The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis.
• The influence of surface energy on stress-free microstructures in shape memory alloys
• Rigidity of branching microstructures in shape memory alloys
• A quantitative rigidity result for the cubic-to-tetragonal phase transition in the geometrically linear theory with interfacial energy
• Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model
• A rigidity result for a perturbation of the geometrically linear three‐well problem
• H-measures, a new approach for studying homogenisation, oscillations and concentration effects in partial differential equations
• Microlocal defect measures
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• On the relation of a three-well energy
• Surface energy and microstructure in coherent phase transitions
• ON THE DEGREE OF RATIONAL APPROXIMATION OF MEROMORPHIC FUNCTIONS
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