论文标题

自适应时空维度降低并发多尺度损害分析

Adaptive Spatiotemporal Dimension Reduction in Concurrent Multiscale Damage Analysis

论文作者

Deng, Shiguang, Apelian, Diran, Bostanabad, Ramin

论文摘要

并发多尺度损伤模型通常用于量化制造诱导的微孔孔度对宏观金属组件损伤响应的影响。但是,这些模型受到主要数值问题的挑战,包括网格依赖性,收敛难度和浓度区域的准确性较低。我们做出了两项贡献,旨在解决这些困难。首先,我们为非线性组成型模型开发了一种新型的自适应组件无impl-expex(AAF-IE)时间整合方案。该方案防止使用隐式算法来模拟软化时会产生的收敛问题。我们的AAF-IE方案自主调整步骤大小,以捕获相关的历史依赖变形。它还可以在用于弹性塑性和损坏模型的运行时重新组装刚度矩阵,从而大大减少了记忆足迹。其次,我们提出了一种基于自适应聚类的域分解策略,以通过将近距离有限元节点聚集到有限数量的群集中,从而大大降低空间自由度。我们的自适应聚类方案具有静态和动态阶段,分别在离线和在线分析过程中进行。自适应策略根据空间不连续性确定簇密度,并通过现场估计控制自适应簇。如数值实验所证明的那样,提出的自适应方法在断裂模拟的效率和准确性之间取得了良好的平衡。特别是,我们使用有效的并发多尺度模型来量化空间变化的显微镜孔隙度对宏结构软化行为的重要性。

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.

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