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.
翻译:硬磁软材料(HMSM)是颗粒复合材料,由含有高残余磁诱导颗粒的软矩阵组成,由高残余磁感应颗粒组成。由于外部磁通量的应用诱导了HMSMM中一对夫妇的身体,这些材料中的Cauchy应激拉一般是不对称的。因此,可以使用微极连续理论来捕捉这些材料的变形。另一方面,HMSMM的地理和结构往往与身体的整体尺寸相比,具有很小的厚度。因此,在目前的贡献中,采用了10度微极外壳配方,以模拟HMSMM制造的薄体结构的有限弹性变形,并受磁刺激的制约。目前的外壳配方可以使用三维结构法,而无需修改即可将平面应力假设应用于薄体结构。由于管理方程式的高度非线性性质,因此也开发出一种非线性有限元素来进行数字模拟。在大规模变形时,采用了一种强化的微波形配方配方。开发的形状的性能通过若干个数值模型来进行模拟。模拟变形的变形模型,以显示其成型的变形。它的变形。它显示为变形的变形。