Among the broad spectrum of active and multifunctional materials, the subclass of ferroic materials are particularly interesting candidates to potentially enable novel applications in, e.g., actuation, sensing, transducing, and data storage applications, due to their unique response properties triggered by the complex multiscale interplay of ferromagnetic (spontaneous magnetisation), ferroelectric (spontaneous
polarisation), or ferroelastic (spontaneous straining) mechanisms.

The purpose of the current work is the discussion of different approaches to the modelling and simulation of microstructure evolution.  Emphasis is placed on formulations which do not resolve the microstructure evolution in space, unlike phase-field or level-set methods, but rather on efficient mixture-type continuum theories that account for the underlying phases and crystallographic variants, with
the related volume fractions restricted by inequality constraints. Such models can be formulated in the context of so-called laminate-based frameworks.

The presentation focuses on the modelling of two particular examples of ferroic materials, namely ferroelectrics and magnetic shape memory alloys.  Different modelling approaches shall be discussed, such as dissipation potential based evolution equations and application of a convexification method as well as rank-one relaxation.