Finite Strain Formulation of the Discrete Equilibrium Gap Principle: I-Mechanically Consistent Regularization for Large Motion Tracking

The equilibrium gap principle offers a good trade-off between robustness & accuracy for regularizing motion tracking, as it simply enforces that the tracked motion corresponds to a body deforming under arbitrary loadings. This paper introduces an extension of the equilibrium gap principle in the large deformation setting, a novel regularization term to control surface tractions, both in the context of finite element motion tracking, and an inverse problem consistent reformulation of the tracking problem. Tracking performance of the proposed method, with displacement resolution down to the pixel size, is demonstrated on synthetic images representing various motions with various signal-to-noise ratios