Identification of mechanical properties of isotropic and anisotropic materials that demonstrate non-linear elastic behavior, such as rubbers and soft tissues of human body, is critical for many industrial and medical purposes. In this paper, a method is presented to obtain the mechanical constants of Mooney-Rivlin and Holzapfel hyper-elastic material models which are employed to describe the behavior of isotropic and anisotropic hyper-elastic materials, respectively. By using boundary measured data from a sample with non-standard geometry, and by using an iterative inverse analysis technique, the material constants are obtained. The method uses the results of different experiments simultaneously to obtain the material parameters more accurately. The effectiveness of the proposed method is demonstrated through three examples. In the two first examples, the simulated measured data are used, while in the third example, the experimental data obtained from a polyvinyl alcohol sample are used.

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Identification of material properties of hyper-elastic materials such as soft tissues of the human body or rubber-like materials has been the subject of many works in recent decades. Boundary conditions generally play an important role in solving an inverse problem for material identification, while their knowledge has been taken for granted. In reality, however, boundary conditions may not be available on parts of the problem domain such as for an engineering part, e.g., a polymer that could be modeled as a hyper-elastic material, mounted on a system or an in vivo soft tissue. In these cases, using hypothetical boundary conditions will yield misleading results. In this paper, an inverse algorithm for the characterization of hyper-elastic material properties is developed, which takes into consideration unknown conditions on a part of the boundary. A cost function based on measured and calculated displacements is defined and is minimized using the Gauss–Newton method. A sensitivity analysis is carried out by employing analytic differentiation and using the finite element method (FEM). The effectiveness of the proposed method is demonstrated through numerical and experimental examples. The novel method is tested with a neo–Hookean and a Mooney–Rivlin hyper-elastic material model. In the experimental example, the material parameters of a silicone based specimen with unknown boundary condition are evaluated. In all the examples, the obtained results are verified and it is observed that the results are satisfactory and reliable.

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