A RATE-INDEPENDENT MODEL FOR THE ISOTHERMAL QUASI-STATIC EVOLUTION OF SHAPE-MEMORY MATERIALS

DOI10.1142/S0218202508002632zbMath1151.74319arXiv0708.4378OpenAlexW2963689079WikidataQ59901902 ScholiaQ59901902MaRDI QIDQ3521619

Ulisse Stefanelli, Alexander Mielke, Ferdinando Auricchio

Publication date: 26 August 2008

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.4378

Mathematics Subject Classification ID

Variational inequalities (49J40) Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05)

Related Items (30)

Existence and linearization for the Souza-Auricchio model at finite strains ⋮ QUASISTATIC ISOTHERMAL EVOLUTION OF SHAPE MEMORY ALLOYS ⋮ Magnetic shape-memory alloys: thermomechanical modelling and analysis ⋮ An energetic formulation of a one-dimensional model of superelastic SMA ⋮ A phenomenological model for the magneto-mechanical response of single-crystal magnetic shape memory alloys ⋮ A macroscopic model for magnetic shape-memory single crystals ⋮ A Preisach type model for temperature driven hysteresis memory erasure in shape memory materials ⋮ Variational formulation and stability analysis of a three dimensional superelastic model for shape memory alloys ⋮ Gradient structures for the thermomechanics of shape-memory materials ⋮ A novel approach to representative orientation distribution functions for modeling and simulation of polycrystalline shape memory alloys ⋮ Energetic formulation for rate-independent processes: remarks on discontinuous evolutions with a simple example ⋮ Viscous corrections of the time incremental minimization scheme and visco-energetic solutions to rate-independent evolution problems ⋮ An incremental energy minimization state update algorithm for 3D phenomenological internal-variable SMA constitutive models based on isotropic flow potentials ⋮ A phenomenological model for microstructure-dependent inelasticity in shape-memory alloys ⋮ Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials ⋮ The Souza-Auricchio model for shape-memory alloys ⋮ Numerical Approximation Techniques for Rate-Independent Inelasticity ⋮ MAGNETIC SHAPE MEMORY ALLOYS: THREE-DIMENSIONAL MODELING AND ANALYSIS ⋮ \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems ⋮ Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints ⋮ Finite Plasticity in $P^\top\!P$. Part II: Quasi-Static Evolution and Linearization ⋮ 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 ⋮ Existence and time-discretization for the finite-strain Souza-Auricchio constitutive model for shape-memory alloys ⋮ Rate-independent processes in viscous solids at small strains ⋮ Numerical approaches to rate-independent processes and applications in inelasticity ⋮ A variational characterization of rate-independent evolution ⋮ Existence and non-existence for the full thermomechanical Souza-Auricchio model of shape memory wires ⋮ BV solutions and viscosity approximations of rate-independent systems ⋮ Convergence analysis of a local stationarity scheme for rate-independent systems

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