Construction of a fairly-priced, embedded domain based mechanical model for image registration
Résumé
With the development of Computed Micro-Tomography (μ-CT), it has become possible to inspect thephysical reality of materials with complex microstructures. One of the main applications of this non-invasive imaging tool in the experimental mechanics community is Digital Image Correlation (DIC),which is a well-known inverse problem also named image registration in, e.g., the computer vision andmedical fields. This method allows to measure strain fields by minimizing a distance of similarity be-tween different image configurations of materials. The DIC problem is ill-posed in Hadamard’s sense,namely, it cannot be solved pixel wise without considering some regularization. When images do notexhibit sufficient gray-level gradient values, which is the case of cellular materials for example, the situa-tion meets its most critical level. Our contribution concerns the development of a general DIC algorithmwhich identifies complex deformations in cellular materials. For that, we constructed an automated andfairly-priced image based mechanical model that accurately describes the mechanical behavior of thecomplex microstructure and used it as a regularization of the inverse problem. This technique, inspiredfrom the work by R ́ethor ́e et al. [1], consists of penalizing the internal elastic forces of the geometryrepresented by the image. Provided a level-set description of the material’s boundary [3], we show thatthe Finite Cell Method [2] introduces an interesting computational context for Digital Image Correlation.In fact, when using higher order B-splines as an approximation basis, along with advanced quadratureschemes, it is possible to measure accurate strain fields that could not be obtained using traditional linearfinite element DIC algorithms