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：本文提出了一种基于新开发的卷积有限元（C-FE）逼近的全局数字图像相关（DIC）方法。该卷积逼近可依托线性有限元网格，在不增加自由度的前提下实现任意高阶近似。因此，基于C-FE的DIC方法能比传统基于FE的DIC方法更精确，可在相同单元尺寸下提供高度平滑且精准的位移与应变结果。本文详细讨论了该方法的公式构建与实现过程。方法中的控制参数包括多项式阶数、补丁尺寸及扩张系数，并探讨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2.0基准问题）对提出的DIC方法进行测试，并与传统基于FE的DIC方法进行对比。在所有测试案例中，C-FE方法均优于FE方法。本研究展示了C-FE的潜力，为全场地位移与应变测量提供了实现高度平滑、精确且鲁棒的DIC分析的新途径。