Quantifying the anisotropic linear elastic behavior of solids

•The anisotropic material property together with the material axis distribution of a solid is mapped non-destructively by solving inverse problem.•The anisotropic material property distribution has been recovered well in the presence of less than 3% noise.•An analytical mathematical model has been successfully applied to explain why the parameter C12 is mapped worse than other material parameters. In this work, we present a non-destructive approach to characterize the heterogeneous mechanical behavior of anisotropic elastic solids. This approach is based on iterative inverse algorithms using the framework of finite element discretization schemes. We test the proposed approach with several theoretical studies and observe that for a low noise level in measured displacement fields, it is possible to map the anisotropic linear elastic parameter distributions with high accuracy. We also observe that with additional displacement field measurements, the solution to the inverse problem becomes more unique. However, for higher noise levels (3%), the quality of the reconstructions deteriorates for the parameter C12 of the orthotropic elasticity tensor. A theoretical analysis is performed and we demonstrate that this may be due to small gradients of the objective function with respect to C12. Overall, the proposed approach has potential to characterize the anisotropic mechanical behavior of polymer based materials or tissues for pathology. [Display omitted]