3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such ForewordThe present paper aims at reviewing the major developments in Digital Volume Correlation (DVC) over the past ten years. It follows the first review on DVC that was published in 2008 by its pioneer [11]. In the latter, the interested reader will find all the general principles associated with what is now called local DVC. They will not be recalled hereafter. In such approaches the region of interest is subdivided into small subvolumes that are independently registered. In addition to its wider use with local approaches, DVC has been extended to global approaches in which the displacement field is defined in a dense way over the region of interest. Kinematic bases using finite element discretizations have been selected. To further add mechanical content, elastic regularization has been introduced. Last, integrated approaches use kinematic fields that are constructed from finite element simulations with chosen constitutive equations. The material parameters (and/or boundary conditions) then become the quantities of interest.These various implementations assume different degrees of integration of mechanical knowledge about the analyzed experiment. First and foremost, DVC can be considered as a stand-alone technique, which has seen its field of applications grow over the last ten years. In this case the measured displacement fields and post-processed strain fields are reported. With the introduction of finite element based DVC, the measured displacement field is continuous. It is also a standalone technique. However, given the fact that it shares common kinematic bases with numerical simulations, it can be easily combined with the latter. One route is to require local satisfaction of equilibrium via mechanical regularization. Another route is to fully merge DVC analyses and numerical simulations via integrated approaches. Different examples will illustrate how these various integration steps can be tailored and what are the current challenges associated with various approaches.

This paper presents a new regularization scheme for Digital Image Correlation(DIC) and Digital Volume Correlation (DVC) techniques based on the equilibrium gap method with reference to a linear elastic behavior. This scheme constitutes a unique framework for performing the so-called mechanical regularization for any problem dimension. "Complete regularization" refers to the fact that a specific treatment of boundaries (surfaces) is introduced here on the same footing as the bulk, independently of the complexity of their shape. The proposed treatment distinguishes the roles that different boundaries (Neumann or Dirichlet) play in mechanical tests. Numerical cases on synthetic data and a real experimental test validate the robustness and accuracy of the method. The analyzed experiment shows that only the use of (complete) regularization ensures convergence. Even in the cases where such regularization is not employed but convergence is achieved, it is at much higher cost. These results reveal the benefit of regularization on the convergence rate of DVC.