Concurrent multiscale damage models are often used to quantify the impacts of manufacturing-induced micro porosity on the damage response of macroscopic metallic components. However, these models are challenged by major numerical issues including mesh dependency, convergence difficulty, and low accuracy in concentration regions. We make two contributions that collectively aim to address these difficulties. Firstly, we develop a novel adaptive assembly free impl-exp (AAF-IE) temporal integration scheme for nonlinear constitutive models. This scheme prevents the convergence issues that arise when implicit algorithms are employed to model softening. Our AAF-IE scheme autonomously adjusts step sizes to capture intricate history dependent deformations. It also dispenses with reassembling the stiffness matrices amid runtime for elasto-plasticity and damage models which, in turn, dramatically reduces memory footprints. Secondly, we propose an adaptive clustering-based domain decomposition strategy to dramatically reduce the spatial degrees of freedom by agglomerating close-by finite element nodes into a limited number of clusters. Our adaptive clustering scheme has static and dynamic stages that are carried out during offline and online analyses, respectively. The adaptive strategy determines the cluster density based on spatial discontinuity and controls adaptive clusters via field estimations. As demonstrated by numerical experiments the proposed adaptive method strikes a good balance between efficiency and accuracy for fracture simulations. In particular, we use our efficient concurrent multiscale model to quantify the significance of spatially varying microscopic porosity on a macrostructural softening behavior.

翻译：并发多尺度损伤模型常用于量化制造引起的微孔隙对宏观金属构件损伤响应的影响。然而，这些模型面临诸多数值难题，包括网格依赖性、收敛困难以及集中区域精度较低等问题。本文提出两项贡献以共同应对上述挑战。首先，我们针对非线性本构模型开发了一种新型自适应无组装显式-隐式（AAF-IE）时域积分方案。该方案避免了隐式算法在模拟软化过程中产生的收敛问题。AAF-IE方案可自主调整步长以捕捉复杂的历史依赖变形，并无需在运行时为弹塑性及损伤模型重新组装刚度矩阵，从而大幅降低内存占用。其次，我们提出了一种基于自适应聚类的区域分解策略，通过将邻近有限元节点聚合为有限数量的簇，显著缩减空间自由度。该自适应聚类方案包含静态和动态两个阶段，分别用于离线和在线分析。自适应策略基于空间不连续性确定簇密度，并通过场估计控制自适应聚类。数值实验表明，所提出的自适应方法在断裂模拟中实现了效率与精度的良好平衡。特别是，我们利用高效并发多尺度模型量化了空间变化的微观孔隙度对宏观结构软化行为的重要影响。