A micropolar shell model for hard-magnetic soft materials

TL;DR

This paper develops a 10-parameter micropolar shell model for simulating the finite elastic deformation of thin hard-magnetic soft materials under magnetic stimuli, incorporating nonlinear finite element methods for accurate numerical analysis.

Contribution

It introduces a novel micropolar shell formulation tailored for HMSMs, enabling effective simulation of their deformation with existing 3D constitutive laws and addressing nonlinearities and large distortions.

Findings

The formulation accurately predicts deformation of HMSMs under magnetic stimuli.

Numerical examples demonstrate the model's effectiveness and robustness.

Enhanced assumed strain approach reduces locking at large distortions.

Abstract

Hard-magnetic soft materials (HMSMs) are particulate composites that consist of a soft matrix embedded with particles of high remnant magnetic induction. Since the application of an external magnetic flux induces a body couple in HMSMs, the Cauchy stress tensor in these materials is asymmetric, in general. Therefore, the micropolar continuum theory can be employed to capture the deformation of these materials. On the other hand, the geometries and structures made of HMSMs often possess small thickness compared to the overall dimensions of the body. Accordingly, in the present contribution, a 10-parameter micropolar shell formulation to model the finite elastic deformation of thin structures made of HMSMs and subject to magnetic stimuli is developed. The present shell formulation allows for using three-dimensional constitutive laws without any need for modification to apply the plane stress assumption in thin structures. Due to the highly nonlinear nature of the governing equations, a nonlinear finite element formulation for numerical simulations is also developed. To circumvent locking at large distortions, an enhanced assumed strain formulation is adopted. The performance of the developed formulation is examined in several numerical examples. It is shown that the proposed formulation is an effective tool for simulating the deformation of thin bodies made of HMSMs.