## Grant GA15-12227S
1.1.2015 - 31.12.2017

Grantor: Czech Science Foundation (GAČR)

### Analysis of mathematical models of multifunctional materials with hysteresis

**Objectives**:

The project topic is mathematical modeling, analysis, and numerical simulations of processes taking place in multifunctional materials with hysteresis. The results will include (1) a rigorous derivation of systems of ordinary and partial differential equations based on physical principles and experimentally verified constitutive relations, (2) proofs of existence, and possibly also uniqueness and stability of solutions to the equations, and (3) their numerical approximation including error bounds. The main applications will involve piezoelectric and magnetostrictive materials used as sensors, actuators, and energy harvestors, as well as thermoelastoplastic materials subject to material fatigue. The presence of hysteresis makes all these steps challenging, also because hysteresis nonlinearities are non-differentiable, which creates difficulties both in the analysis and in the numerics. New algorithms will have to be developed to treat the problems in maximal complexity.