Experimental determination of the parameters of the nonlinearly elastic Hencky model

Abstract

This work presents a variant of physically nonlinear constitutive elasticity relations derived using the Hencky strain tensor. A test plant for determining the model’s constants is designed. These constants for weakly compressible materials are derived by compression tests of prismatic elastomeric specimens. The results of solving the problem of indentation of a rigid spherical stamp into a cylindrical specimen are provided. The suggested constitutive relations were used with the constants found by the compression tests. In addition, calculations were performed according to the relations known for the Hencky material and to the hypoelasticity relations with the neutral derivative of the stress tensor. To stabilize the calculation procedures, the Hencky tensor and its derivative were expanded by the monotonous parameter in a series by the Cauchy strain tensor degrees without any restrictions for allowable strain values. A numerical algorithm was built for tracking the variable area of contact. The calculation procedures of discretizing the stated problem by the finite elements method and step-by-step loading were implemented as an applied software suite. One of the integral characteristics of the process considered was the indentation curve defined as the dependence of the stamp immersion effort on the stamp immersion depth. The curves derived by computation are compared with the data of the indentation test conducted on the designed plant. It has been shown that the calculations according to the Hencky model and hypoelasticity relations provide a fair description of the curve to strains of around 30%. The suggested physical nonlinear model allows describing the continued strain growth to a sufficient degree of accuracy.