Global existence for the three-dimensional Frémond model of shape memory alloys

DOI10.1016/0362-546X(94)00097-2zbMath0832.35066MaRDI QIDQ4839273

Pierluigi Colli

Publication date: 26 February 1996

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

shape memory alloysthermo-mechanical modelmartensitic phase transitionssemi-implicit time discretizationFrémond model

Mathematics Subject Classification ID

Stefan problems, phase changes, etc. (80A22) A priori estimates in context of PDEs (35B45) Theoretical approximation in context of PDEs (35A35)

Related Items (18)

A dissipative model for hydrogen storage: existence and regularity results ⋮ Error Control Of A Nonlinear Evolution Problem Related To Phase Transitions ⋮ Magnetic shape-memory alloys: thermomechanical modelling and analysis ⋮ Attractors for a three-dimensional thermo-mechanical model of shape memory alloys ⋮ Collisions in shape memory alloys ⋮ Optimal Control for Shape Memory Alloys of the One-Dimensional Frémond Model ⋮ Structure result for steady-state solutions of a one-dimensional Frémond model of SMA ⋮ The Souza-Auricchio model for shape-memory alloys ⋮ Error Estimates for a Variable Time-Step Discretization of a Phase Transition Model with Hyperbolic Momentum ⋮ Global solution to a Frémond model for shape memory alloys with thermal memory ⋮ Mesoscopic model of microstructure evolution in shape memory alloys, its numerical analysis and computer implementation ⋮ Well-posedness of a thermo-mechanical model for shape memory alloys under tension ⋮ Existence of solutions for a mathematical model related to solid-solid phase transitions in shape memory alloys ⋮ An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys ⋮ A three-dimensional model of the thermomechanical behavior of shape memory alloys ⋮ Uniqueness results for the full Frémond model of shape memory alloys ⋮ Existence and non-existence for the full thermomechanical Souza-Auricchio model of shape memory wires ⋮ Analysis of a variable time-step discretization of the three-dimensional Frémond model for shape memory alloys

Cites Work

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• On a nonlinear system for shape memory alloys
• Stationary solutions for the one-dimensional Frémond model of shape memory effects
• Global existence for a second-order thermo-mechanical model of shape memory alloys
• Positivity of temperature in the general Frémond model for shape memory alloys
• Existence and uniqueness of global solutions to an extended model of the dynamical developments in shape memory alloys
• Thermo-mechanical evolution of shape memory alloys
• Global existence for a three-dimensional model for the thermo-mechanical evolution of shape memory alloys
• Global solution to the full one‐dimensional Frémond model for shape memory alloys

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