Towards Eliminating the Displacement Bias Due to Out‐Of‐Plane Motion in 2D Inverse Problems: A Case of General Rigid‐Body Motion

This article reports an important development related to the inverse characterization of material constitutive parameters using 2D optical displacement field measurements. The out‐of‐plane motion of the specimen, which has traditionally been considered detrimental to the accuracy of these experiments, is generally of two types: (a) a global out‐of‐plane rigid‐body motion of the specimen relative to the camera and (b) out‐of‐plane deformations resulting from material heterogeneity or out‐of‐plane loads. In an earlier article, we proposed to partially relax the condition of no out‐of‐plane motion by allowing for (b) in 2D inverse procedures, in the context of finite element update method, and introduced a compensation strategy by redefining the cost function on the object plane of the acquisition system. The experimental errors due to (a) were assumed negligible. Here, we propose that the global rigid‐body motion (a) may also be recovered within the inverse procedures, hence completely waiving the condition of strictly in‐plane displacements for inverse problems. The recovery is achieved by identifying and including the possible modes of global rigid‐body motion within the cost function together with careful selection of test configuration. The effects of individual rigid‐body modes on the computed displacement fields are studied in detail and utilized as a guideline for selection of test configuration. The approach is fully demonstrated and validated by simulated as well as real experiments for determining elastic constants of isotropic and orthotropic materials using different experimental setups. Effects of improving the optimization routine, for cost function minimization, and experimental noise are also presented.