Magneto-visco-hyperelasticity for hard-magnetic soft materials: theory and numerical applications

Soft materials that can deform under external stimuli offer great opportunities for the development of new structural applications such as sensor-actuator systems, soft robots or biomedical devices. Among these materials, soft polymers filled with magnetic particles are experiencing an increasing interest from the scientific community. Apart from magnetorheological elastomers and ferrogels, a new magneto-sensitive material type has been developed recently. These so-called hard-magnetic materials allow for shape-programmability by the addition of magnetically-hard particles within a polymeric matrix. In this regard, constitutive and computational frameworks describing the magneto-mechanics of such materials are needed to provide new avenues in the development of novel applications based on hard-magnetic soft polymers. To this end, this work focuses on the mathematical modelling of the magneto-mechanics of hard-magnetic soft materials and their implementation in finite element (FE) frameworks. The proposed continuum model is formulated for large deformations and within a thermodynamically consistent framework. In addition, the model incorporates viscous contributions to account for relaxation and dissipation effects in the deformation process of these materials when subjected to external magnetic fields and/or mechanical loading. To illustrate the theory, the magneto-mechanical model is implemented within an implicit static FE framework and three numerical examples are provided to explore potential applications as well as to evaluate the influence of the external magnetic field application on the viscoelastic response of the material. Finally, the framework is implemented in an implicit dynamic FE framework to evaluate the role of inertial terms on the dynamic response of these materials.