当前位置: X-MOL 学术Finite Elem. Anal. Des. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A three-field based finite element analysis for a class of magnetoelastic materials
Finite Elements in Analysis and Design ( IF 3.5 ) Pub Date : 2024-02-03 , DOI: 10.1016/j.finel.2024.104126
Tao Jin

A simple yet effective material model was proposed by Zhao et al. (2019) and demonstrated to be capable of modeling the shape transformations of various planar and three-dimensional material samples programmed with the so-called “hard-magnetic soft materials”. Based on the aforementioned material model, this paper aims to further accomplish the following two tasks. First, a detailed analysis is performed to investigate the impact of the multiplicative volumetric-distortional split of the deformation gradient tensor applied to the material magnetic energy. Through a trivial boundary value problem, the impact of the volumetric-distortional split is quantified for the strictly incompressible material and the nearly incompressible material, respectively. Second, a finite element procedure based on the three-field variational principle, or the mixed displacement-Jacobian-pressure formulation (Simo et al., 1985; Simo and Taylor, 1991), is developed for the magnetoelastic materials programmed with complex magnetic patterns. Even though the finite element formulation based on the three-field variational principle is a standard and widely adopted technique in the literature, the introduction of the multiplicative split of the deformation gradient into the magnetic energy makes the derivation of the specific finite element terms less trivial. In this work, the finite element formulation and the consistent linearization of the coupled system are derived in detail for the Newton–Raphson iterations. Through the theoretical analysis and numerical examples, the approach based on the distortional part of the deformation gradient is shown to possess computational advantages over its counterpart in the context of a relatively simple penalty method. Moreover, the convergence behaviors of the finite element simulations and the impact of the finite element spaces on the pressure oscillation are analyzed in detail.

中文翻译:

一类磁弹性材料的基于三场的有限元分析

赵等人提出了一种简单而有效的材料模型。(2019)并证明能够对用所谓的“硬磁软材料”编程的各种平面和三维材料样本的形状变换进行建模。基于上述材料模型,本文旨在进一步完成以下两个任务。首先,进行详细分析以研究应用于材料磁能的变形梯度张量的乘法体积扭曲分裂的影响。通过一个简单的边值问题,分别量化了严格不可压缩材料和近不可压缩材料的体积扭曲分裂的影响。其次,针对采用复杂磁模式编程的磁致弹性材料,开发了基于三场变分原理或混合位移雅可比压力公式(Simo 等人,1985;Simo 和 Taylor,1991)的有限元程序。 。尽管基于三场变分原理的有限元公式是文献中广泛采用的标准技术,但将变形梯度乘法分裂引入磁能使得特定有限元项的推导不再那么简单。在这项工作中,详细推导了牛顿-拉夫森迭代的有限元公式和耦合系统的一致线性化。通过理论分析和数值算例,表明基于变形梯度畸变部分的方法在相对简单的惩罚方法中比其对应方法具有计算优势。此外,还详细分析了有限元模拟的收敛行为以及有限元空间对压力振荡的影响。
更新日期:2024-02-03
down
wechat
bug