有限应变弹塑性标定技术的比较研究：面向FEMU和VFM的数值精确灵敏度分析
A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM
AI总结：
本研究通过数值精确灵敏度严格比较VFM与FEMU在有限应变弹塑性参数校准中的表现，并测试其鲁棒性。
摘要：
材料参数的准确识别对于计算力学中的预测建模至关重要。实验力学界从全场数字图像相关数据中校准参数的两种主要方法被称为有限元模型更新（FEMU）和虚拟场方法（VFM）。在VFM中，目标函数是内部与外部虚功或虚功率之间的平方失配。在FEMU中，目标函数量化了模型预测与相应实验测量的感兴趣量之间的加权失配，并通过迭代更新有限元模型参数来最小化。虽然FEMU被认为更灵活，但VFM因其计算开销显著更低而常被用来替代FEMU。然而，两种方法之间的比较通常涉及通过有限差分方案对梯度或灵敏度进行近似，从而使得直接评估变得困难。因此，在本研究中，我们在通过局部灵敏度分析和自动微分软件获得的数值精确灵敏度的背景下，严格比较VFM和FEMU。为此，两种方法均在有限应变弹塑性模型上进行了测试。我们开展了一系列测试案例，以评估两种方法在实际挑战下的鲁棒性。
英文摘要：
Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. The two primary approaches in the experimental mechanics' community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we rigorously compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, both methods are tested on a finite strain elastoplasticity model. We conduct a series of test cases to assess both methods' robustness under practical challenges.
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