Constitutive Modelling and Parameter Identification for Rubber-Like Materials

The aim of the paper is to determine the phenomenological model to characterize the stress-strain relation and to simulate the behaviour of solid polyurethane (PUR) rubbers used in civil engineering, as well as to present the process of identification of model parameters for such materials. For the material studied the strain energy density function was established and a general constitutive relationship for the second-order tensor of Piola–Kirchhoff stress for elasticity is determined. Constitutive relationships for engineering stress in terms of the principal stretches are also specified. The paper presents the method of identification of parameters for constitutive models of hyperelasticity and hypoelasticity for the accessible experimental data. The applied identification procedure is based on the feature of two-phase structure of polyurethane material and is supported by the experimental data from uniaxial quasi-static tension and compression tests. In the analysis, the material behaviour was considered both for the case of incompressible deformation and also for the case of slightly compressible, nonlinearly elastic materials that are homogeneous and isotropic. The change of volume was admitted too, in range of large deformations in a tension and compression test. The attempt of description of stress-softening phenomenon was undertaken in rubber-like materials, for a given level of strain, under unloading (the Mullins effect) caused by the damage of microstructure of this material. Different descriptions of the stress-softening phenomenon were already proposed in the literature but they fail to give fully satisfactory conformity of experimental data with theoretical predictions. The phenomenological model by Elias–Zúñiga and Beatty, A new phenomenological model for stress-softening in elastomers, ZAMP, 53, 794–814, 2002, for such materials was modified by different softening functions and a simplified version of this model was identified, based on the experimental data. In the proposed model, the damage of microstructure was described by a new exponential function, which depends on the current magnitude of intensity of strain and its earlier maximum value during the process of material loading. In this paper, a suitable analysis of existent models and their verification based on experimental data for polyurethane rubber is presented for uniaxial experiments. It is shown that the magnitude of stress-softening varies with strain and this phenomenon increases with the magnitude of the pre-strain and the type of loading: monotonic tension, compression or cyclic loading. The obtained results are presented graphically for uniaxial tension and compression.