This manuscript presents a multiscale reduced-order modeling framework for heterogeneous materials that accounts for both cohesive interface failure and continuum damage. The model builds on the eigendeformation-based reduced-order homogenization model (EHM), which relies on the pre-calculation of a set of coefficient tensors that account for the effects of linear and nonlinear material behavior between regions of the domain known as parts. A k-means clustering algorithm is used to optimally construct these parts and a new formulation for the partitioning of interfaces using this method is proposed. The extraction of the volumetric and interfacial influence functions is performed using the Interface-enriched Generalized Finite Element Method (IGFEM), which relies on a finite element discretization that does not conform to the material phase boundaries. A Lagrange multiplier method is used in this preprocessing phase, allowing for the reuse of the matrix factorization for different influence function problems and hence leading to efficiency improvement. A newly proposed traction calculation for the interface partition is also adopted to alleviate the instability caused by traction calculations along interfaces. The accuracy and efficiency of the IGFEM–EHM method is assessed through comparison with reference IGFEM simulations. The method is then used to extract the nonlinear multiscale response of particulate, unidirectional fiber-reinforced, and woven composites.

该手稿提出了一种用于异质材料的多尺度降阶建模框架，该框架可解决内聚界面失效和连续损伤。该模型建立在基于本征变形的降阶均质化模型（EHM）的基础上，该模型依赖于一组系数张量的预先计算，这些系数张量考虑了称为零件的区域之间线性和非线性材料行为的影响。使用k-means聚类算法来优化构造这些部分，并提出了使用该方法进行接口划分的新公式。体积和界面影响函数的提取是使用富含界面的广义有限元方法（IGFEM）进行的，它依赖于不符合材料相边界的有限元离散化。在此预处理阶段中，使用了拉格朗日乘数法，可以将矩阵分解用于不同的影响函数问题，从而提高效率。还采用了针对接口分区的新提议的牵引力计算来减轻沿接口的牵引力计算所引起的不稳定性。通过与参考IGFEM仿真进行比较，评估了IGFEM-EHM方法的准确性和效率。然后，该方法用于提取颗粒，单向纤维增强和机织复合材料的非线性多尺度响应。允许矩阵分解重新用于不同的影响函数问题，从而提高效率。还采用了针对接口分区的新提议的牵引力计算来减轻沿接口的牵引力计算所引起的不稳定性。通过与参考IGFEM仿真进行比较，评估了IGFEM-EHM方法的准确性和效率。然后，该方法用于提取颗粒，单向纤维增强和机织复合材料的非线性多尺度响应。允许矩阵分解重新用于不同的影响函数问题，从而提高效率。还采用了针对接口分区的新提议的牵引力计算来减轻沿接口的牵引力计算所引起的不稳定性。通过与参考IGFEM仿真进行比较，评估了IGFEM-EHM方法的准确性和效率。然后，该方法用于提取颗粒，单向纤维增强和机织复合材料的非线性多尺度响应。通过与参考IGFEM仿真进行比较，评估了IGFEM-EHM方法的准确性和效率。然后，该方法用于提取颗粒，单向纤维增强和机织复合材料的非线性多尺度响应。通过与参考IGFEM仿真进行比较，评估了IGFEM-EHM方法的准确性和效率。然后，该方法用于提取颗粒，单向纤维增强和机织复合材料的非线性多尺度响应。