Reduced order models for the nonlinear response of heterogeneous microstructures typically require a construction (or training) stage to build the reduced order basis. In this manuscript, an efficient model construction strategy for the eigenstrain homogenization method (EHM) is presented. The proposed strategy relies on a parallel, element-by-element, conjugate gradient solver. Near linear scaling has been achieved with respect to the number of degrees of freedom used to resolve the microstructure. Linear scaling with respect to the number of pre-analyses required to construct the reduced order model (ROM) follows from the EHM formulation. Furthermore, a parallel implementation for fast evaluation of the constructed ROM has been developed using shared memory parallelization. It has been shown that for large microstructures with $\approx 10,000$ grains, the total computational cost of evaluating the nonlinear response of a polycrystal could be reduced by approximately an order of magnitude using 32 cores with respect to serial ROM simulation. The present methodology has been verified using an additively manufactured polycrystalline microstructure of a nickel-based superalloy, Inconel 625. The capability of the developed framework to construct a ROM for such large microstructures, as well as the ability of the ROM to predict average and local quantities of interest has been demonstrated.

用于异质微结构非线性响应的降阶模型通常需要构建（或训练）阶段来构建降阶基础。在本手稿中，提出了特征应变均质化方法（EHM）的有效模型构建策略。所提出的策略依赖于并行、逐元素、共轭梯度求解器。在用于解析微观结构的自由度数量方面已经实现了近线性缩放。构建降阶模型 (ROM) 所需的预分析数量的线性缩放遵循 EHM 公式。此外，还使用共享内存并行化开发了一种用于快速评估所构造 ROM 的并行实现。已经表明，对于具有$\approx 10,000$使用 32 个内核，相对于串行 ROM 模拟，评估多晶非线性响应的总计算成本可以减少大约一个数量级。目前的方法已经使用镍基高温合金 Inconel 625 的增材制造多晶微观结构进行了验证。所开发的框架能够为如此大的微观结构构建 ROM，以及 ROM 预测平均和局部的能力已经证明了感兴趣的数量。