Visco-hyperelastic Analysis And Nonlinear Stiffness Calculation Of Package Damping Rubber

In the circulation of goods,especially in the long-term transportation of precision equipment,the implementation of packaging cushioning and vibration reduction design is of great significance to prevent packaging failure and protect goods.Rubber material is widely used as packaging damping material because of its excellent hyperelasticity,damping and fatigue resistance.The visco-hyperelastic of the vibration damping rubber and nonlinear stiffness calculation of the vibration damping rubber products is an important direction of long-term attention and continuous research in academia and engineering.This paper focuses on the complex mechanical behavior and constitutive model of damping rubber materials under cyclic tension,the viscoelastic behavior under static and dynamic loads,and the simulation method of nonlinear stiffness of products.The specific research contents and conclusions are as follows:(1)Uniaxial cyclic tension,biaxial cyclic tension,planar cyclic tension and volume compression tests are carried out on vibration damping rubber materials,and the test results are analyzed.The results show that the damping rubber material exhibits not only the typical hyperelastic behavior,but also the stress softening behavior,permanent deformation and variable volume behavior under cyclic tensile load.The typical behaviors of the damping rubber under cyclic tensile load are simulated by using the relevant constitutive equations,and a method to describe the complex mechanical behavior of the material is determined.Taking an hourglass shock absorber as an example,the load-displacement curve of the device under compression load is calculated and verified by experiments.The results show that the calculation results considering the hyperelasticity,stress softening and permanent deformation of damping rubber materials are in good agreement with the experimental results.(2)By comparing the characterization ability of the viscoelastic Maxwell model,Kelvin model and their generalized models on the creep behavior of damping rubber materials,a modified viscoelastic constitutive model is constructed based on the generalized Maxwell model and Ogden hyperelastic model.This model can describe the whole process of step loading,relaxation or creep of the damping rubber materials,and can predict the static viscoelastic behavior under various loading modes.Taking an hourglass shock absorber as an example,the creep behavior of the device under constant compression load is simulated using the modified viscoelastic model.The results show that the modified viscoelastic constitutive model can well simulate the creep behavior of the shock absorber,and verified by experiments.(3)Based on the influence of dumbbell shaped and rectangular samples on the test results of the dynamic mechanical properties,dumbbell shaped rubber sample is selected to test the changes of storage modulus and loss modulus with frequency under different prestrain and strain amplitude values.Combined with the test data of rubber uniaxial tension,plane tension and equibiaxial tension,the parameters used to simulate the mechanical behavior of viscoelastic materials in frequency domain were determined.And the storage stiffness,loss stiffness and dynamic stiffness of a typical rubber shock absorber at different frequencies are calculated,it is found that the dynamic stiffness of rubber shock absorber is V-shaped with the change of frequency,and the minimum stiffness develops towards higher frequency with the increase of pre compression.(4)The rubber cutting experiment and the plane tensile crack growth experiment were carried out.By piecewise fitting the crack growth length and the cycle curve,the relationship curve between the crack growth rate and the tear energy is obtained,and the fatigue threshold,turning tear energy and critical tear energy of the damping rubber material are quickly obtained.The fatigue threshold is consistent with the value determined by the cutting experiment.The influence of preload and stiffness on fatigue life is calculated by using the determined fatigue characteristic parameters.It is found that appropriate preload can effectively improve the fatigue life of products.Increasing the stiffness within the design allowable range can greatly improve the fatigue life of shock absorbers,but has little impact on the vibration reduction effect.