Measuring displacement and strain fields at low observable scales of complex microstructures still remains a challenge in experimental mechanics often because of the combination of low definition images with poor texture at this scale. This is the case for cellular materials, for which complex local phenomena can occur. The aim of this paper is to design and validate numerically and experimentally a Digital Image Correlation (DIC) technique for the measurement of local displacement fields of samples with complex cellular geometries (i.e samples presenting multiple random holes). It consists of a DIC method assisted with a physically sound weak regularization using an elastic B-spline image-based model. This technique introduces a separation of scales above which DIC is dominant and below which it is assisted with image-based modeling. Several in-silico experimentations are performed in order to finely analyze the influence of the introduced regularization lengths for different input mechanical behaviors (elastic, elasto-plastic and geometrically non-linear) and in comparison with true error quantification. We show that the method can estimate complex local displacement and strain fields with speckle-free low definition images, even in non-linear regimes such as local buckling or plasticity. Finally, an experimental validation is proposed in 2D-DIC to allow for the comparison of the proposed method on low resolution speckle-free images with a classic DIC on speckled high resolution images.

The integration of numerical simulation and experimental measurements in cellular materials at the sub-cellular scale is a real challenge. On the experimental side, the almost absence of texture makes displacement fields measurement tricky. On the simulation side, it requires the construction of reliable and specimen-specific geometric and mechanical models from digital images. For this purpose, high order based fictitious domain approaches have proven to be an efficient alternative to boundary conforming finite elements for the analysis of geometrically complex objects. A number of discretization parameters needs to be set by the user by making a trade-off between accuracy and computational cost. In addition to numerical errors (interpolation, integration etc.), there are additional geometric and model errors due to the pixelation of the image (e.g., quantization, sampling, noise). In the literature, discretization parameters are often analyzed without taking pixelation into account, which can lead to over-calculations. In this paper, these parameters are adjusted to obtain (a) the best possible accuracy (bounded by pixelation errors) while (b) ensuring minimal complexity (concept of fair price). In order to analyze the different sources of error, various two-dimensional synthetic experiments are generated by mimicking the image acquisition process from high-resolution numerical simulations considered as a reference. The approach leads to a modeling that outperforms conventional approaches both in terms of accuracy and complexity. Eventually, it is shown that the presented image-based models provide a unique opportunity to assist digital volume correlation and allow the measurement of relevant local kinematics within cellular materials.