An Enhanced Micro-Spring Constitutive Model of Metal Rubber

Abstract

Metal rubber (MR), as a new hysteresis non-linear elastic material with unique properties, has been extensively used in recent years, especially in aviation, aerospace and harsh conditions while the relevant theoretical research is still in the initial stage. In this paper, an effective constitutive model is established to describe the nonlinear mechanical behaviour and complex micro-contact frictional phenomena of MR. An adaptive deformation micro-spring element with random spatial distribution is adopted in this model based on the irregular overlapping, interlacing and force-deformation characteristics of metal wire material. The laws of load deformation and the frictional contact of the MR wires are considered in the model. Starting from the micro-spring force, an enhanced constitutive model including macroscopic parameters, such as shape factor, relative density, filament diameter and spiral coil diameter of MR, and microstructural parameters, such as spatial orientation angle of wires, the ratio of the micro-spring states and friction coefficient is developed for the first time. The feasibility of the enhanced constitutive model is verified by comparing the analytical results computed by the theoretical model, the numerical results of dynamic simulation based on the virtual prototype model, and the experimental results of MR under unidirectional tests. Finally, the accuracy of the model is conducted through being compared with the porous material model and the curved cantilever beam model. The results demonstrated that the characteristics of MR, especially its nonlinear stiffness, are well modelled in the enhanced micro-spring model.