Boundary conditions identification in problems of hyper-elastic materials deformation

In this study, by an inverse method, which uses the Tikhonov regularization method, traction boundary conditions on the surface of a hyper-elastic material are determined. Displacements at several points on the surface of the body are measured and used to find the unknown stress parameters on a part of the problem boundary. The inverse analysis is carried out for Mooney-Rivlin and Ogden isotropic models. An example for identification of boundary conditions on a boundary part of a two dimensional domain with a relatively complicated geometry is presented to show the effectiveness of the proposed method. Effects of different parameters are studied in this example. The results for both hyper-elastic models show that the error of the solution decreases with increasing the number of measured data and decreasing the measurement error. Moreover, it is observed that the accuracy of the solution is decreased when the nonlinear behavior of the material is increased.