Bifurcation and metastability in a new one-dimensional model for martensitic phase transitions

DOI10.1016/S0045-7825(98)00205-9zbMath0949.74049OpenAlexW2125277973MaRDI QIDQ1965155

Phoebus Rosakis, Anna Vainchtein, Timothy J. Healey

Publication date: 11 December 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(98)00205-9

zbMATH Keywords

hysteresislocal bifurcation analysislocal energy minimazero interfacial energyphase nucleationglobal-bifurcation diagramsone-dimensional model for twinningstress-induced martensitic phase transitionstwo-well nonconvex elastic energy density

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Bifurcation and buckling (74G60) Problems involving hysteresis in solids (74N30)

Related Items (4)

Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations ⋮ BIFURCATION AND STABILITY OF MARTENSITIC TRANSFORMATION DYNAMICS ⋮ Unconditionally stable, second-order schemes for gradient-regularized, non-convex, finite-strain elasticity modeling martensitic phase transformations ⋮ Bifurcations in the regularized Ericksen bar model

Uses Software

• AUTO
• AUTO-86

Cites Work

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• Structured phase transitions on a finite interval
• Equilibrium of bars
• Singular perturbations as a selection criterion for periodic minimizing sequences
• On the dynamics of fine structure
• On higher order gradient continuum theories in 1-D nonlinear elasticity. Derivation from and comparison to the corresponding discrete models
• Finite-scale microstructures and metastability in one-dimensional elasticity
• The role of the spinodal region in one-dimensional martensitic phase transitions

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