Active (smart/intelligent) materials are designed to respond with a defined expansion behavior to a multi-field stimulus. In the current work, we present the Stimulus-Expansion-Model (SEM) that allows the unified formulation of active behavior for different classes of active materials, such as piezoceramics, hydrogels, and dielectric elastomers. Different formulations with respect to geometric (non)linearity, material (non)linearity, multisensitivity, non-scalar stimulus, and transient/dynamic behavior, are presented. They are derived from the physics of the materials or in a data-driven way from experiments. Furthermore, the implementation – in the current work, the application of the SEM description in the framework of analytical descriptions or in finite element simulation tools – is discussed. Even though the SEM leads to very specialized models with a limited field of validity for each material class, this method is helpful for highlighting the similarities between active materials. It allows engineers to design combined active-passive structures for specific applications without the need of a specialized (multi-field) software tool. It thus opens up the field of smart materials, and active-passive composites, to a much wider community.