Finite deformation analysis of hard-magnetic soft materials based on micropolar continuum theory

Abstract

Hard-magnetic soft materials (HMSMs), as a sub-class of magneto-active polymers, consist of a polymeric matrix filled with particles of high remnant magnetic induction. The application of external magnetic flux on HMSMs induces a moment on its material particles. From the angular momentum balance law, it is deduced that the Cauchy stress tensor in these materials cannot be symmetric. Therefore, the micropolar continuum theory, with inherent asymmetric stress tensor, is a rational candidate for modeling the deformation of these materials. In the present contribution, an HMSM is modeled as a three-dimensional micropolar continuum body, which is subjected to external magnetic stimuli. The moment resulting from the interaction of the internal and external magnetic fluxes plays the role of a body couple in the micropolar formulation. After developing the main formulation, due to the highly nonlinear nature of the governing equations, the weak form of the equations and its linearization to perform numerical simulations is presented. To demonstrate the capability and performance of the developed formulations, several examples are provided. It is shown that the present formulation can successfully predict the deformation of HMSMs under various loading and boundary conditions.