The influence of surface energy on stress-free microstructures in shape memory alloys

DOI10.1007/BF01557083zbMath0835.73061OpenAlexW1998077739MaRDI QIDQ1905576

Stefan Müller, Georg Dolzmann

Publication date: 10 January 1996

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01557083

zbMATH Keywords

variational methodspseudo-elasticityminimization of elastic energysolid-solid phase transformationexistence of stress-free microstructures

Mathematics Subject Classification ID

Micromechanics of solids (74M25) Micromechanical theories (74A60) Phase transitions (general) in equilibrium statistical mechanics (82B26)

Related Items (16)

A rigidity result for a reduced model of a cubic-to-orthorhombic phase transition in the geometrically linear theory of elasticity ⋮ The cubic-to-orthorhombic phase transition: rigidity and non-rigidity properties in the linear theory of elasticity ⋮ On the two-state problem for general differential operators ⋮ Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity ⋮ Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(K^{lc}) ⋮ On rigidity for the four-well problem arising in the cubic-to-trigonal phase transformation ⋮ A class of nonlinear elasticity problems with no local but many global minimizers ⋮ Origin of stabilization of macrotwin boundaries in martensites ⋮ Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates ⋮ Quantitative Aspects of the Rigidity of Branching Microstructures in Shape Memory Alloys via H-Measures ⋮ Rigidity of branching microstructures in shape memory alloys ⋮ Higher Sobolev regularity of convex integration solutions in elasticity: the planar geometrically linearized hexagonal-to-rhombic phase transformation ⋮ On the energy scaling behaviour of a singularly perturbed Tartar square ⋮ Rigidity and flexibility in the modelling of shape-memory alloys ⋮ Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations ⋮ On a probabilistic model for martensitic avalanches incorporating mechanical compatibility

Cites Work

• Fine phase mixtures as minimizers of energy
• Self-accommodation in martensite
• Energy minimizers for large ferromagnetic bodies
• Microstructures with finite surface energy: The two-well problem
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
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