Global existence result for thermoviscoelastic problems with hysteresis

DOI10.1016/j.nonrwa.2011.07.018zbMath1238.35157OpenAlexW2045849828MaRDI QIDQ420079

Laetitia Paoli, Adrien Petrov

Publication date: 20 May 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.07.018

zbMATH Keywords

maximal monotone operatorsheat equationplasticityshape-memory alloysexistence resultdoubly nonlinear equationsgeneralized standard materialsenthalpy transformation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence of solutions of dynamical problems in solid mechanics (74H20) Problems involving hysteresis in solids (74N30) PDEs in connection with mechanics of deformable solids (35Q74) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (6)

Magnetic shape-memory alloys: thermomechanical modelling and analysis ⋮ Structure-preserving finite difference scheme for 1D thermoviscoelastoplastic equations under uniformly distributed temperature ⋮ Nonlinear dynamic response of a simply-supported Kelvin-Voigt viscoelastic beam, additionally supported by a nonlinear spring ⋮ The Souza-Auricchio model for shape-memory alloys ⋮ Existence of solutions of a thermoviscoplastic model and associated optimal control problems ⋮ Global solutions to phase change models with heat transfer for a class of smart materials

Cites Work

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• The free energy of mixing for \(n\)-variant martensitic phase transformations using quasi-convex analysis
• Nonlinear elliptic and parabolic equations involving measure data
• An upper bound to the free energy of mixing by twin-compatible lamination for \(n\)-variant martensitic phase transformations
• Compact sets in the space \(L^ p(0,T;B)\)
• Three-dimensional model for solids undergoing stress-induced phase transformations
• A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals
• A variational formulation of rate-independent phase transformations using an extremum principle
• Comparison of isotropic hardening and kinematic hardening in thermoplasticity
• Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters
• On rate-independent hysteresis models
• On the formulation of coupled thermoplastic problems with phase change.
• \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems
• Quasistatic evolution problems for linearly elastic-perfectly plastic materials
• Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
• Thermodynamics of Rate-independent Processes in Viscous Solids at Small Strains
• EXISTENCE AND UNIQUENESS RESULTS FOR A CLASS OF RATE-INDEPENDENT HYSTERESIS PROBLEMS
• Thermo-visco-elasticity at small strains with 𝐿¹-data
• Boundary-value problems for the system of elasticity theory in unbounded domains. Korn's inequalities
• Strongly nonlinear elliptic equations having natural growth terms and L1 data
• Quasistatic Problems in Viscoplasticity Theory I: Models with Linear Hardening
• Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformations
• RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY
• A three‐dimensional model describing stress‐temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications
• A model for temperature-induced phase transformations in finite-strain elasticity
• Existence results for a class of rate-independent material models with nonconvex elastic energies
• Thermoviscoplasticity at small strains

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