Comparison of the geometrically nonlinear and linear theories of martensitic transformation

DOI10.1007/BF01126525zbMath0780.73005WikidataQ59718351 ScholiaQ59718351MaRDI QIDQ687180

Kaushik Bhattacharya

Publication date: 30 January 1994

Published in: Continuum Mechanics and Thermodynamics (Search for Journal in Brave)

zbMATH Keywords

crystalline solidsnonlinear thermoelasticity

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Micromechanics of solids (74M25) Stefan problems, phase changes, etc. (80A22) Micromechanical theories (74A60)

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Cites Work

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• The torsion problem for a nonconvex stored energy function
• Reconciliation of local and global symmetries of crystals
• Weak Martensitic transformations in Bravais lattices
• On \(\nu +1\)-lattices
• Displacive phase transformations in solids
• Constitutive theory for some constrained elastic crystals
• Fine phase mixtures as minimizers of energy
• Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid
• Equilibrium configurations of crystals
• Some phase transitions in crystals
• Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: An example
• On the symmetry of deformable crystals
• Discontinuous deformation gradients away from the tip of a crack in anti- plane shear
• Anti-plane shear fields with discontinuous deformation gradients near the tip of a crack in finite elastostatics
• Characterizations of Young measures generated by gradients
• Self-accommodation in martensite
• Compact zones of shear transformation in an anisotropic solid
• The relaxation of a double-well energy
• The determination of the elastic field of an ellipsoidal inclusion, and related problems
• Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities
• Special Topics in Elastostatics
• Korn’s inequality for sequences
• ELASTIC MATERIALS WITH TWO PREFERRED STATES
• Proposed experimental tests of a theory of fine microstructure and the two-well problem
• On Korn's inequality