On nonlinear thermo-magneto-electro-elasticity and FE analysis of magneto-electro-elastic structures

Multiphase magneto-electro-elastic (MEE) materials are obtained either by combining piezoelectric and piezomagnetic particles/fibers in bulk form or laminated form (i.e. stacking piezoelectric and piezomagnetic layers) to accomplish required full magneto-electro-mechanical coupling. Such structures exhibit a four-way coupling effect between the mechanical, electrical, magnetic and thermal quantities. In the majority of papers available in literature this coupling is taken into account only in the constitutive equations. It is however well known that truly coupled analysis should also be based on the interaction of the mechanical, thermal, electro-static and magneto-static quantities in the field equation. Due to coupling of the mechanical, electric, magnetic and thermal variables in the field equations non-classical effects occur, like e.g. heating due to compression, cooling due to stretching, and damping of vibrations due to heat loss as well as field rate dependent change of temperatures. A thermodynamically consistent continuum mechanics based framework is developed, which includes the conservation of mass, linear and angular momentum and the conservation of energy. The second principle of thermodynamics is used to derive the restrictions for the constitutive equations using the Coleman-Noll analysis approach. The resulting set of equations is more general and valid for a wider class of problems than most models published in literature. By means of finite element simulations the effect of thermo-mechanical-electro-magnetic coupling is demonstrated.