Hard-magnetic soft (HMS) beams made of soft polymer matrix embedded with hard-magnetic particles can generate large and fast deformation under magnetic stimulation. Dynamic modeling and simulation of HMS beams interacting with complex environment are challenging in terms of computational accuracy and efficiency. This paper presents a method for high-order modeling and efficient computation of HMS beams. The major contribution of the method is a new three-node HMS beam element of absolute nodal coordinate formulation (ANCF), which applies to two material models of nonlinear and linear elasticities (i.e. neoHookean and St. Venant-Kirchhoff) coupled with magnetic energy. To improve the efficiency of the method, the paper presents how to derive the generalized internal forces and their Jacobians via invariant tensors, and how to determine the generalized external forces to model dynamic loads and interactions including gravity, hydrodynamics in fluids, and frictional contact in pipelines. Afterwards, the paper gives both static and dynamic equations with Rayleigh damping and discusses the numerical algorithms. Finally, the paper makes a comparison of static analysis and the experimental observation to validate the accuracy of the proposed modeling method. The paper also discusses the dynamic simulations, including forced vibration, swimming motion, crawling locomotion, and navigating motion to demonstrate the predictive capability and efficacy of the proposed method for dynamic problems.

中文翻译：

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通过 ANCF 高阶有限元对硬磁软梁与环境相互作用的动态建模和仿真


由嵌入硬磁颗粒的软聚合物基体制成的硬磁软（HMS）梁可以在磁刺激下产生大而快速的变形。 HMS梁与复杂环境相互作用的动态建模和仿真在计算精度和效率方面具有挑战性。本文提出了一种 HMS 梁的高阶建模和高效计算方法。该方法的主要贡献是绝对节点坐标公式（ANCF）的新三节点HMS梁单元，适用于与磁能耦合的非线性和线性弹性两种材料模型（即neoHookean和St. Venant-Kirchhoff）。为了提高该方法的效率，本文介绍了如何通过不变张量导出广义内力及其雅可比行列式，以及如何确定广义外力来模拟动态载荷和相互作用，包括重力、流体中的流体动力学以及流体中的摩擦接触管道。随后，本文给出了瑞利阻尼的静态和动态方程，并讨论了数值算法。最后，本文进行了静态分析和实验观察的比较，验证了所提出的建模方法的准确性。本文还讨论了动态模拟，包括受迫振动、游泳运动、爬行运动和导航运动，以证明所提出的方法对动态问题的预测能力和有效性。