Mono-scale and multi-scale formulations of gradient-enriched dynamic piezomagnetics

In this contribution, we combine and extend earlier work on static piezomagnetics and dynamic gradient elasticity to develop novel dynamic piezomagnetic continuum models. The governing equations can be formulated as a mono-scale model or as multi-scale models. The latter include full coupling between micro and macro-scale displacements and micro and macro-scale magnetic potentials, which allows to denote these as “multi-scale multi-physics” models. The field equations and boundary conditions are given together with the underlying energy functionals. An analysis of coupled dispersive waves is carried out to illustrate the behaviour of the models and their ability to simulate dispersive piezomagnetic waves.