Identifying simultaneously hyper-viscoelastic parameters from a unique heterogenous relaxation test: application to engineering elastomeric materials

In this study, the hyper-viscoelastic behavior of elastomeric specimen is identified, from only one heterogeneous test. The test consists on stretching a cruciform specimen in two perpendicular directions and holding at the stretched level to characterize relaxation. The constitutive model is based on the Yeoh model and the Prony series to describe the hyperelastic and viscous behaviors, respectively. In the first part of the paper, a sensitivity analysis is carried out, to optimize the displacement and displacement rate to be prescribed in the identification procedure in order to increase the identifiability of the constitutive parameters. The identification procedure is based on the Finite Element Model Updating (FEMU) technique. While the test induces heterogeneous kinematic fields, a residual to be minimized is built by considering only measured and predicted reaction forces at one branch end of the specimen. The minimization problem is solved by using the Inverse-PageRank-Particle Swarm Optimization (I-PR-PSO) algorithm. In the second part of the paper, the identification is carried out by applying the previously defined optimized loading conditions to the specimen. A numerical validation was first performed by simulating the relaxation test with different loading conditions. Then, the identification methodology was applied to a real test. The identified parameters were used to satisfactorily predict the mechanical response of the cruciform specimen under a different loading as the one used during the identification procedure.