Mathematical investigation of hysteresis in material modeling

ABSTRACT

The proposed multilateral project aims at modeling hysteresis in multifunctional, porous and granular materials, and in contact problems for deformable solids. Significant examples are piezoelectric and magnetostrictive materials which are widely used as sensors, actuators, and energy harvesters. The mathematical approaches to be used encompass variational inequalities, time discretization techniques, among other analytical tools from the theories of hysteresis and partial differential equations. Their investigation entails the development of efficient and reliable numerical schemes for coupled systems with multiple sources of hysteresis. For the practical application of mathematical models, appropriate strategies are needed for the calibration of the material parameters involved in the constitutive equations.