Micromechanics-based constitutive modeling of hard-magnetic soft materials

Soft materials exhibit large deformation material nonlinearity when stretched and possess enhanced elongation-at-break strain prior to rupture. As a result, these materials can cater to several state-of-the-art biomedical and microfluidic applications that require cross-domain energy transduction. Furthermore, they are often impregnated with external multi-functional filler materials (e.g., hard-magnetic particles) to result in hard-magnetic soft materials (hMSM). This gives rise to an inherent complexity owing to the multi-physics coupling due to magnetics and solid dynamics (along with geometric and material nonlinearities), which demands a rigorous magneto-mechanical model for a thorough understanding of their large deformation mechanical behavior under magneto-mechanical loads. It is also mandatory to understand their rate-dependent, hyperelastic, and flow behavior that is omnipresent during their deformation process. This paper focuses on the development of a novel thermodynamically-consistent micromechanics-based constitutive model that incorporates all these attributes using the finite deformation theory. A statistical mechanics-based approach has been undertaken to model the mechanics of the elastomer matrix. The plastic behavior due to the elastomer and the dispersed magnetic phases has been further accounted using a double-yield function with a micromechanical approach. The developed model shows a good agreement for a wide range of hMSM subjected to a variety of complex loading conditions. Finally, a parametric study has been carried out to provide physical insights into the different model parameters.