We present a new eigendeformation-based reduced order homogenization approach for simulating progressive degradation and failure in brittle composite materials. A new reduced model basis construction strategy is proposed, where the bases are based on numerically calculated “failure paths” within the material microstructure subjected to a pre-selected set of load configurations. The failure paths are allowed to overlap, leading to a slight deviation from orthonormality of the basis functions of the reduced order model. In order to alleviate the spurious post failure residual stresses, we propose a new hierarchical failure path update approach, where the influence functions are adaptively updated to incorporate compatible eigenstrains as microstructural failures are detected. The reduced order modeling approach is verified against particulate composite microstructures with ordered and random configurations. The proposed approach leads to significant improvements in accuracy, while maintaining a low model order.

中文翻译：

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降阶计算均质化的失效路径方法

我们提出了一种新的基于特征变形的降阶均质化方法，用于模拟脆性复合材料的渐进退化和失效。提出了一种新的简化模型基础构建策略，其中基础是基于在承受一组预选载荷配置的材料微观结构内通过数值计算的“失效路径”。允许故障路径重叠，导致与降阶模型的基函数的正交性略有偏差。为了减轻虚假的失效后残余应力，我们提出了一种新的分层失效路径更新方法，其中在检测到微观结构失效时自适应地更新影响函数以合并兼容的本征应变。降阶建模方法针对具有有序和随机配置的颗粒复合微结构进行了验证。所提出的方法显着提高了准确性，同时保持了低模型阶数。