The identification of the parameters of the mechanic-geometrical model under uniaxial tension of the highly elastic material

Abstract

The method of construction and identification of the mechanical-geometrical model is presented. The model is used in order to obtain new constitutive assumption for nonlinear elastic materials under severe deformations. According to the proposed method, the deformation of the elementary volume of the elastic continuum in the form of a cube is determined by the force interactions between the faces of the cube. These interactions are modeled by a system of bonds, which reacts an exterior load by and then transfer them to each face of the elementary volume. The bonds in this construction have different mechanical properties, characterized by stiffness (or elasticity) coefficients. These bonds are the generalized estimations of internal force interactions within the material, but not the real forces of interatomic or intermolecular interactions, studied by physicochemical methods. Thus, the model, describing the deformations of the continuous medium, is a geometry construction from the deformed rods (built in the elementary volume) providing corresponding bonds. Constitutive assumptions of the elastic model in the main axes for the case of triaxial deformation are formed up in the article. The general procedure of the identification of the model’s parameters under triaxial deformation and the identification procedure based on the experimental data for uniaxial stretching of the elastomers, taking into account there incompressibility are worked out. The characteristics of the model’s bonds rigidities were restored for two types of experimental curves of elastomers’ stretching (monotonically increasing and S-type curves). Polynominal dependences of the bond hardness from the elongation of the corresponding bond were selected for purposes of testing of the corresponding method of the identification. The obtained stretching curves for a model accord well with the experimental data. The graphs demonstrating the behavior of the identified functions of the bonds’ rigidities and the inner reactions of the bonds depending on the size of its elongation are also included. The graphs of the specific potential energy of the straining of a nonlinear media correspondent with two types of elastomers mentioned above are presented as well. The 3D surface graphs relate to the case of flat deformation of the incompressible material, and the 2D curves — to uniaxial stretching of the same material. The graphs of the energy are convex and this is the evidence of the physically reasonable basis of the method of a modelling.