This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space-time parametric problems. The method has been successfully applied to parametric elastic-plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy has been presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.

翻译：本文提出了一种扩展张量分解（XTD）模型降阶方法。该方法基于对传统张量分解进行稀疏非分离式富集，有望改善高度非线性和奇异情况下的逼近精度与可约化性（可压缩性）。所提出的XTD方法可成为求解非线性时空参数化问题的有力工具，并已成功应用于参数化弹塑性问题以及具有不确定性量化的实时增材制造残余应力预测。此外，本文进一步提出了结合XTD与自洽聚类分析（SCA）的多尺度材料建模策略，从而实现了实时多尺度多参数仿真。通过与有限元分析的对比，验证了该方法的有效性与效率。所提方法为面向不确定性的快速制造与材料设计提供了全新框架。