This study presents a robust numerical method for the computational homogenization analysis of microstructures at limit state. The periodic boundary conditions for asymmetric meshes are effectively handled using piecewise cubic Hermite interpolation. The accuracy of the numerical results is greatly enhanced through the utilization of the edge-based smoothed finite element method (ES-FEM) enriched with a cubic bubble function. The bubble-enhanced ES-FEM (bES-FEM) is also able to avoid volumetric locking induced by the incompressibility constraints in plane strain limit analysis. The optimization problem is formulated as conic programming and is rapidly solved using primal-dual interior point-based software packages. Adaptive mesh refinement offers substantial benefits in reducing computational costs and predicting the failure mechanism of microscopic heterogeneous materials. The interaction surface of the effective macroscopic strengths can also be rapidly and directly obtained. Investigation of various representative volume elements (RVE) with arbitrary mesh designs demonstrates the computational efficacy of the proposed method.

中文翻译：

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使用自适应 bES-FEM 进行非对称微结构产量设计的计算均质化

这项研究提出了一种稳健的数值方法，用于极限状态下微观结构的计算均质化分析。使用分段三次 Hermite 插值可以有效处理非对称网格的周期性边界条件。通过使用富含三次气泡函数的基于边缘的平滑有限元法（ES-FEM），数值结果的准确性大大提高。气泡增强 ES-FEM (bES-FEM) 还能够避免平面应变极限分析中不可压缩约束引起的体积锁定。优化问题被表述为圆锥规划，并使用基于原对偶内点的软件包快速求解。自适应网格细化在降低计算成本和预测微观异质材料的失效机制方面提供了巨大的好处。还可以快速、直接地获得有效宏观强度的相互作用面。对具有任意网格设计的各种代表性体积单元（RVE）的研究证明了所提出方法的计算功效。