This work presents a novel global digital image correlation (DIC) method, based on a newly developed convolution finite element (C-FE) approximation. The convolution approximation can rely on the mesh of linear finite elements and enables arbitrarily high order approximations without adding more degrees of freedom. Therefore, the C-FE based DIC can be more accurate than {the} usual FE based DIC by providing highly smooth and accurate displacement and strain results with the same element size. The detailed formulation and implementation of the method have been discussed in this work. The controlling parameters in the method include the polynomial order, patch size, and dilation. A general choice of the parameters and their potential adaptivity have been discussed. The proposed DIC method has been tested by several representative examples, including the DIC challenge 2.0 benchmark problems, with comparison to the usual FE based DIC. C-FE outperformed FE in all the DIC results for the tested examples. This work demonstrates the potential of C-FE and opens a new avenue to enable highly smooth, accurate, and robust DIC analysis for full-field displacement and strain measurements.

翻译：本文提出了一种新颖的全局数字图像相关（DIC）方法，该方法基于新开发的卷积有限元（C-FE）近似。卷积近似可依托线性有限元网格实现，并能在不增加自由度的前提下提供任意高阶的近似。因此，在相同单元尺寸下，基于C-FE的DIC方法能提供高度平滑且精确的位移与应变结果，其精度优于常规的基于有限元的DIC方法。本文详细阐述了该方法的公式推导与实现过程。方法中的控制参数包括多项式阶数、补丁尺寸和膨胀系数。文中讨论了参数的一般选择原则及其潜在的自适应性。通过多个代表性算例（包括DIC挑战赛2.0基准问题）对所提出的DIC方法进行了测试，并与常规的基于有限元的DIC方法进行了对比。在所有测试算例的DIC结果中，C-FE均优于有限元方法。本研究展示了C-FE的潜力，为全场位移与应变测量开辟了一条实现高度平滑、精确且鲁棒的DIC分析的新途径。