An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension

DOI10.1016/j.jmps.2011.12.006zbMath1244.74056arXiv0910.2538OpenAlexW2158657503MaRDI QIDQ443697

Zongxi Cai, Hui-Hui Dai

Publication date: 13 August 2012

Published in: Journal of the Mechanics and Physics of Solids (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.2538

zbMATH Keywords

phase transitionsasymptotic analysisthin stripinstabilitiesbifurcations of PDE's

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Experimental work for problems pertaining to mechanics of deformable solids (74-05) Bifurcation and buckling (74G60) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (4)

Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations ⋮ Pitchfork and octopus bifurcations in a hyperelastic tube subjected to compression: Analytical post-bifurcation solutions and imperfection sensitivity ⋮ Analytical study on the stress-induced phase or variant transformation in slender shape memory alloy samples ⋮ On a consistent dynamic finite-strain shell theory and its linearization

Cites Work

• Unnamed Item
• Unnamed Item
• Phase transitions induced by extension in a slender SMA cylinder: analytical solutions for the hysteresis loop based on a quasi-3D continuum model
• Instabilities induced by phase transformation fronts coalescence during the phase transitions in a thin SMA layer: mechanism and analytical descriptions
• On constructing the analytical solutions for localizations in a slender cylinder composed of an incompressible hyperelastic material
• Finite element simulations of martensitic phase transitions and microstructures based on a strain softening model
• Thermodynamics of shape memory alloy wire: Modeling, experiments, and application
• Micromechanical modeling of stress-induced phase transformations. I: Thermodynamics and kinetics of coupled interface propagation and reorientation
• Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. II: Study of the individual phenomena
• A continuum model of a thermoelastic solid capable of undergoing phase transitions
• Equilibrium of bars
• A thermodynamical constitutive model for shape memory materials. I: The monolithic shape memory alloy
• A thermodynamical constitutive model for shape memory materials. II: The SMA composite material
• Simulations of localized thermo-mechanical behavior in a NiTi shape memory alloy.
• Nonlinear stability analysis of pre-stressed elastic bodies.
• Elliptic-Spline Solutions for Large Localizations in a Circular Blatz–Ko Cylinder Due to Geometric Softening
• Phase transitions in a slender cylinder composed of an incompressible elastic material. I. Asymptotic model equation
• Phase transitions in a slender cylinder composed of an incompressible elastic material. II. Analytical solutions for two boundary-value problems
• Asmptoticaliy Approximate Model Equations for Weakly Nonlinear Long Waves in Compressible Elastic Rods and their Comparisons with Other Simplified Model Equations
• Asymptotic Bifurcation Solutions for Compressions of a Clamped Nonlinearly Elastic Rectangle: Transition Region and Barrelling to a Corner-like Profile

This page was built for publication: An analytical study on the instability phenomena during the phase transitions in a thin strip under uniaxial tension