A review on material models for isotropic hyperelasticity  

作　　者：Stephen K.Melly Liwu Liu Yanju Liu Jinsong Leng 

机构地区：[1]Department of Astronautical Science and Mechanics,Harbin Institute of Technology(HIT),Harbin,China [2]Center for Composite Materials and Structures,Harbin Institute of Technology(HIT),Harbin,China

出　　处：《International Journal of Mechanical System Dynamics》2021年第1期71-88,共18页国际机械系统动力学学报（英文）

基　　金：National Natural Science Foundation of China,Grant/Award Number:11772109。

摘　　要：Dozens of hyperelastic models have been formulated and have been extremely handy in understanding the complex mechanical behavior of materials that exhibit hyperelastic behavior(characterized by large nonlinear elastic deformations that are completely recoverable)such as elastomers,polymers,and even biological tis-sues.These models are indispensable in the design of complex engineering com-ponents such as engine mounts and structural bearings in the automotive and aerospace industries and vibration isolators and shock absorbers in mechanical systems.Particularly,the problem of vibration control in mechanical system dy-namics is extremely important and,therefore,knowledge of accurate hyperelastic models facilitates optimum designs and the development of three‐dimensional finite element system dynamics for studying the large and nonlinear deformation beha-vior.This review work intends to enhance the knowledge of 15 of the most com-monly used hyperelastic models and consequently help design engineers and scientists make informed decisions on the right ones to use.For each of the models,expressions for the strain‐energy function and the Cauchy stress for both arbitrary loading assuming compressibility and each of the three loading modes(uniaxial tension,equibiaxial tension,and pure shear)assuming incompressibility are pro-vided.Furthermore,the stress–strain or stress–stretch plots of the model's pre-dictions in each of the loading modes are compared with that of the classical experimental data of Treloar and the coefficient of determination is utilized as a measure of the model's predictive ability.Lastly,a ranking scheme is proposed based on the model's ability to predict each of the loading modes with minimum deviations and the overall coefficient of determination.

关 键 词：constitutive models finite deformation HYPERELASTIC mechanical system dynamics strain energy density 

分 类 号：O34[理学—固体力学]