多晶材料的电磁-机械响应：通过虚拟单元法的计算均匀化
Electro-magneto-mechanically response of polycrystalline materials: Computational Homogenization via the Virtual Element Method
摘要：
本文研究了电磁-机械耦合问题的计算均匀化问题。VE方法具有很大的潜力，均匀化的物理性能的异质多晶微结构与各向异性晶粒。如果与有限元（FE）网格相比，可以利用单元形状的灵活性来创建具有显著较低的自由度的VE网格，同时保持高精度。VE方法优于FEM的证据可在文献中获得，但仅解决纯力学问题（即弹性性质）和横向各向异性材料。这项工作的目的是双重的。一方面，研究比较VE和FE为基础的数值均匀化计划的机电耦合问题的不同晶格结构和程度的弹性各向异性。在所有考虑的材料中，对于相同数量的节点，VE方法优于FE方法。另一方面，研究了由机电晶粒和磁机械晶粒组成的混合微结构，从而产生电磁机械耦合的微结构。同样，VEM提供了更准确的解决方案策略。
英文摘要：
This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties of heterogeneous polycrystalline microstructures with anisotropic grains. The flexibility in element shapes can be exploited for creating VE-mesh with a significant lower number of degrees of freedom if compared to finite element (FE) meshes, while maintaining a high accuracy. Evidence that VE-approaches outperform FEM are available in the literature, but only addressing purely-mechanic problems (i.e. elastic properties) and transversely anisotropic materials. The aim of this work is twofold. On one hand, the study compares VE-and FE-based numerical homogenization schemes for electro-mechanically coupled problems for different crystal lattice structures and degrees of elastic anisotropy. Within all considered materials, the VE-approach outperforms the FE-approach for the same number of nodes. On the other hand a hybrid microstructure made up by both electro-mechanical and magneto-mechanical grains is investigated resulting in a electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy.
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