Finite deformations of a carbon black-filled rubber. Experiment, optical measurement and material parameter identification using finite elements

The identification of material parameters occurring in constitutive equations frequently plays a more minor role in large deformations in view of the difficulties encountered when endeavouring to perform specified deformations by means of experiments. This article aims to illustrate special optical measurements obtained with the help of a CCD camera applied to tensile and compression tests, to allow a larger number of measured quantities to be incorporated into the material parameter identification process. Based on these inhomogeneous deformations, we propose an identification procedure founded on a gradient-free optimisation technique which incorporates the finite element method while also taking account of inequality constraints. The finite element method is employed to obtain a numerical solution of the underlying boundary-value problem, which has to be compared with the experimental data pertaining to carbon black-filled rubber in the sense of the least-square method. The proposed procedure is independent of the underlying finite-element programme and is being investigated from the point of view of its performance.