Existence and non-existence for the full thermomechanical Souza–Auricchio model of shape memory wires

0360070 - MÚ 2012 RIV GB eng J - Journal Article
Krejčí, Pavel - Stefanelli, U.
Existence and non-existence for the full thermomechanical Souza–Auricchio model of shape memory wires.
Mathematics and Mechanics of Solids. Roč. 16, č. 4 (2011), s. 349-365. ISSN 1081-2865. E-ISSN 1741-3028
R&D Projects: GA ČR GAP201/10/2315
Institutional research plan: CEZ:AV0Z10190503
Keywords : shape memory alloys * thermomechanics * existence result * blowup in finite time
Subject RIV: BA - General Mathematics
Impact factor: 1.012, year: 2011
http://mms.sagepub.com/content/early/2011/03/11/1081286510386935.abstract

We provide an existence theory for the full thermomechanical quasi-static evolution of a shape memory wire described by the Souza–Auricchio constitutive model. The analysis requires some mild restriction on the choice of the thermomechanical coupling term in the expression on the free energy of the material. This restriction slightly deviates from the original Souza–Auricchio modeling frame, while still being compatible with real situations. We additionally show that, by imposing no such restriction, the original Souza–Auricchio model is ill-posed.
Permanent Link: http://hdl.handle.net/11104/0197708