Abstract The high-fidelity generalized method of cells (HFGMC) enables micromechanical analysis of heterogeneous materials with high accuracy but does so at the cost of computational efficiency. In this paper, an implementation of the triply periodic HFGMC is developed to enable high-resolution simulations of materials with complex microstructures at a significantly reduced computational cost. This paper describes efficient reformulation and develops low-cost algorithms to reduce overall computation time and memory required to analyze complex 3D microstructures. The low-cost algorithms exploit the sparsity of the data by storing and performing calculations on only the non-zero values. The Parallel Direct Sparse Solver (PARADISO) subroutine is used to execute the most computationally intensive processes in parallel on multiple cores. Simulations of two selected test cases demonstrate the validity, computational efficiency, and value of the developed implementation. The results indicate that the savings in computation time and required memory are substantial and more than 100 times in some cases. In addition, parallel processing further reduces the computation time. The efficiency achieved through this work makes the high-resolution simulation of complex microstructures using HFGMC for the prediction of accurate local stress/strain fields computationally feasible.

中文翻译：

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复杂微结构细胞高保真广义方法的有效实现

摘要 细胞的高保真广义方法 (HFGMC) 能够以高精度对异质材料进行微机械分析，但这样做的代价是计算效率。在本文中，开发了三重周期 HFGMC 的实现，以显着降低计算成本对具有复杂微观结构的材料进行高分辨率模拟。本文介绍了有效的重新制定并开发了低成本算法，以减少分析复杂 3D 微观结构所需的总体计算时间和内存。低成本算法通过仅对非零值存储和执行计算来利用数据的稀疏性。Parallel Direct Sparse Solver (PARADISO) 子例程用于在多个内核上并行执行计算量最大的进程。两个选定测试用例的模拟证明了所开发实现的有效性、计算效率和价值。结果表明，计算时间和所需内存的节省是巨大的，在某些情况下超过 100 倍。此外，并行处理进一步减少了计算时间。通过这项工作实现的效率使得使用 HFGMC 对复杂微观结构进行高分辨率模拟来预测准确的局部应力/应变场在计算上是可行的。并行处理进一步减少了计算时间。通过这项工作实现的效率使得使用 HFGMC 对复杂微观结构进行高分辨率模拟来预测准确的局部应力/应变场在计算上是可行的。并行处理进一步减少了计算时间。通过这项工作实现的效率使得使用 HFGMC 对复杂微观结构进行高分辨率模拟来预测准确的局部应力/应变场在计算上是可行的。