A FEM-based direct method for identification of Young's modulus and boundary conditions in three-dimensional linear elasticity from local observation

Simultaneously identifying unknown Young's modulus and boundary conditions of a linear elastic material with the measurements only on a part of its boundary is an inverse problem, which is usually solved by iterative methods in most studies. In this paper, we present a direct inverse method based on the finite element method (FEM) to recover these unknown parameters without iteration. A novel energy-like regularization term is developed to ensure the convergence of the estimated parameters with noisy input. In order to increase the accuracy of estimation, a novel regularization coefficient and its related preprocessing steps are designed based on the Morozov's discrepancy principle to obtain the optimal regularization parameter, which is independent to the observation noise. In numerical experiments, several three-dimensional objects with different shapes and distribution of observed and unknown regions were used to verify the proposed method under different observation noises. Physical experiments were also conducted on a silicone phantom. The results of both numerical and physical experiments successfully recovered the Young's modulus and displacement boundary conditions with expected accuracies close to their corresponding observation noise levels.