On modeling, analytical study and homogenization for smart materials
- Timofte, Aida
2010 Mathematics Subject Classification
- 74H20 74H25 35J85 74C05 74Q05
- Ferroelectrics, shape memory alloys, energetic formulation, evolutionary variational inequalities, homogenization, existence, uniqueness
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.
- Topics on mathematics for smart systems, 237--252, World Sci, Publ., Hackensack, NJ, 2007