A method for determining elastic constants and boundary conditions of three-dimensional hyperelastic materials

Abstract

Although there have been many studies on the identification of elastic constants and boundary conditions, it is still challenging to simultaneously estimate the unknown elastic constants and boundary conditions of a three-dimensional hyperelastic material under locally observed boundary conditions with noise. In this paper, a novel inverse method based on two different objective functions is proposed. The first objective function is constructed by a “dual fields” construction method, which utilizes redundant Cauchy boundary conditions (displacement boundary conditions and force boundary conditions) on the observable boundary. The second objective function is based on the gap between measured and calculated displacements of the observable boundary. The inverse analysis is conducted by an adjoint method and a linear approximation method based on the theories of continuum mechanics and finite element method to obtain the Jacobian matrices of the objective functions with respect to different variables. An alternating iterative algorithm based on Gauss–Newton method is proposed to minimize the objective functions. The proposed inverse algorithm is tested using nearly incompressible Neo-Hookean and nearly incompressible Mooney–Rivlin hyperelastic model in numerical experiments and physical experiments with a silicone-based tissue-mimicking material. The results of both numerical and physical experiments show the feasibility and accuracy of the proposed method.