WIAS Preprint No. 1180, (2006)

On modeling, analytical study and homogenization for smart materials



Authors

  • Timofte, Aida

2010 Mathematics Subject Classification

  • 74H20 74H25 35J85 74C05 74Q05

Keywords

  • Ferroelectrics, shape memory alloys, energetic formulation, evolutionary variational inequalities, homogenization, existence, uniqueness

Abstract

We discuss existence, uniqueness, regularity, and homogenization results for some nonlinear time-dependent material models. One of the methods for proving existence and uniqueness is the so-called energetic formulation, based on a global stability condition and on an energy balance. As for the two-scale homogenization we use the recently developed method of periodic unfolding and periodic folding. We also take advantage of the abstract Gamma convergence theory for rate-independent evolutionary problems.

Appeared in

  • Topics on mathematics for smart systems, 237--252, World Sci, Publ., Hackensack, NJ, 2007

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