A rate-independent model for permanent inelastic effects in shape memory materials

Michela Eleuteri; Luca Lussardi; Ulisse Stefanelli; Michela Eleuteri; Luca Lussardi; Ulisse Stefanelli

doi:10.3934/nhm.2011.6.145

Networks and Heterogeneous Media

2011, Volume 6, Issue 1: 145-165. doi: 10.3934/nhm.2011.6.145

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A rate-independent model for permanent inelastic effects in shape memory materials

1.
Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38100 Povo (Trento)
2.
Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, 44227 Dortmund
3.
Istituto di Matematica Applicata e Tecnologie Informatiche – CNR, Via Ferrata 1, 27100 Pavia

Received: 01 May 2010 Revised: 01 October 2010
Primary: 74C05; 35K86.

This paper addresses a three-dimensional model for isothermal stress-induced transformation in shape memory polycrystalline materials in presence of permanent inelastic effects. The basic features of the model are recalled and the constitutive and the three-dimensional quasi-static evolution problem are proved to be well-posed. Finally, we discuss the convergence of the model to reduced/former ones by means of a rigorous $\Gamma$-convergence analysis.
- Shape memory materials,
- permanent inelastic effects,
- well-posedness,
- $\Gamma$-convergence
Citation: Michela Eleuteri, Luca Lussardi, Ulisse Stefanelli. A rate-independent model for permanent inelastic effects in shape memory materials[J]. Networks and Heterogeneous Media, 2011, 6(1): 145-165. doi: 10.3934/nhm.2011.6.145

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Abstract

This paper addresses a three-dimensional model for isothermal stress-induced transformation in shape memory polycrystalline materials in presence of permanent inelastic effects. The basic features of the model are recalled and the constitutive and the three-dimensional quasi-static evolution problem are proved to be well-posed. Finally, we discuss the convergence of the model to reduced/former ones by means of a rigorous $\Gamma$-convergence analysis.

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