论文标题
抗曲线剪切的松弛微态连续体模型的混合H1XH（卷曲）有限元公式
A hybrid H1xH(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear
论文作者
论文摘要
模拟超材料的一种方法是扩展有关其运动学方程的相关连续性理论，而松弛的微态连续体代表了这样的模型。它在自由能函数中融合了非对称微脱位的卷曲。这表明存在不属于H1的溶液的存在，因此标准的节点H1-元素会产生不令人满意的收敛速率，并且可能无法找到精确的溶液。我们的方法是使用Hilbert Spaces H1和H（Curl）的基础功能，证明了此类组合对于此类问题的核心作用。为简单起见，引入了描述抗平台剪切的二维松弛微态连续体，并保留了三维版本的主要计算特征。然后，该模型用于对可行的有限元解决方案的配方和多步骤研究，其中包括对标准和混合配方的存在和独特性的检查以及各自的收敛速率。
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to H1, such that standard nodal H1-finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces H1 and H(curl), demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates.
