Digital volume correlation (DVC), the volumetric extension of the popular digital image correlation (DIC) technique, is a powerful experimental tool for measuring 3D volumetric full-field displacements and strains. Most current DVC algorithms can be categorized into either local or finite-element-based global methods. As with most experimental approaches, there are drawbacks with each of these methods. In the local method the subvolume deformations are estimated independently and the computed displacement field may not necessarily be kinematically compatible. Thus, the deformation gradients can be noisy, especially when using small volumetric subsets. Although the global method often enforces kinematic compatibility, it generally incurs substantially greater computational costs than its local counterpart, which is especially significant for large volumetric data sets. To address these shortcomings, we present a new hybrid DVC algorithm, called augmented Lagrangian digital volume correlation (ALDVC), which combines the advantages of both the local (fast computation time) and global (compatible displacement field) methods. This new algorithm builds on our recent work on the augmented Lagrangian digital image correlation (2D-ALDIC) technique and solves the general motion optimization problem by using the alternating direction method of multipliers (ADMM). We demonstrate that our ALDVC algorithm has high accuracy and precision while maintaining low computational cost, and is a significant improvement compared to current local and global DVC methods. ALDVC is a computationally efficient algorithm to measure 3D volumetric displacements and strains. An open-source Matlab implementation is freely available.

中文翻译：

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增强拉格朗日数字体积相关 (ALDVC)

数字体积相关 (DVC) 是流行的数字图像相关 (DIC) 技术的体积扩展，是用于测量 3D 体积全场位移和应变的强大实验工具。大多数当前的 DVC 算法可以分为局部或基于有限元的全局方法。与大多数实验方法一样，这些方法中的每一种都有缺点。在局部方法中，子体积变形是独立估计的，计算出的位移场可能不一定是运动学兼容的。因此，变形梯度可能是嘈杂的，尤其是在使用小体积子集时。尽管全局方法通常会强制执行运动学兼容性，但它通常会比其局部方法产生更大的计算成本，这对于大型体积数据集尤其重要。为了解决这些缺点，我们提出了一种新的混合 DVC 算法，称为增强拉格朗日数字体积相关 (ALDVC)，它结合了局部（快速计算时间）和全局（兼容位移场）方法的优点。这种新算法建立在我们最近在增强拉格朗日数字图像相关 (2D-ALDIC) 技术方面的工作基础上，并通过使用乘法器交替方向法 (ADMM) 解决了一般运动优化问题。我们证明了我们的 ALDVC 算法在保持低计算成本的同时具有很高的准确性和精度，并且与当前的局部和全局 DVC 方法相比是一个显着的改进。ALDVC 是一种计算效率高的算法，用于测量 3D 体积位移和应变。