Magneto-active polymers (MAPs) are revolutionising the fields of material science and solid mechanics as well as having an important presence in the bioengineering community. These composites consist of a polymeric matrix (i.e., elastomer) filled with magnetic particles (i.e., iron particles). When bonded together, these two phases form a continuum solid that, under the application of an external magnetic field, mechanically reacts leading to changes in shape and volume or/and alterations in its rheological properties. Such a magneto mechanical response is determined by the material properties of the polymeric matrix and magnetic particles. In this work, we present the mechanical characterisation of MAPs constituted by PDMS filled with carbonyl iron powder (CIP) particles. To this end, sixteen different combinations of elastomeric base/crosslinker mixing ratio (from 5:1 to 20:1) and particles' volume fraction (from 0% to 30%) are tested under tensile loading. These results are analysed and provide the bases for the formulation of a nonlinear constitutive model that accounts for these dependencies. The modelling approach is extended to incorporate magneto-mechanical effects. Finally, the complete model is used to provide theoretical guidance for magneto-active systems, highlighting potential applications in epithelial wound healing stimulation.