Abstract
We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries (phases) are preferred. Furthermore we consider possible large deformations of the crystal lattice. After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings. This article is an overview of [2].
Highlights
We consider the elastic theory of single crystals at constant temperature where the free energy density depends on the local concentration of one or more species of particles in such a way that for a given local concentration vector certain lattice geometries are preferred
After deriving the physical model, we indicate by means of a suitable implicite time discretization an existence result for measure-valued solutions that relies on a new existence theorem for Young measures in infinite settings
A crucial point of the model is that it allows possible large deformations of the crystal lattice that can especially occur at the phase boundaries and for which the assumptions of linear elasiticity theory does not hold
Summary
Citation for published version (APA): Arnrich, S. Discrete and Continuous Dynamical Systems - Series S, 5(1), 29-48. Document Version: Publisher’s PDF, known as Version of Record (includes final page, issue and volume numbers). General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S Volume 5, Number 1, February 2012 doi:10.3934/dcdss.2012.5.29 pp. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS SERIES S Volume 5, Number 1, February 2012 doi:10.3934/dcdss.2012.5.29 pp. 29–48
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