基于Exp-ln模型与广义黏弹性理论的橡胶本构模型及其应用研究
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摘要
提出了一种描述橡胶材料不同应变率下力学响应的黏超弹本构模型。首先,利用Instron实验机和SHTB实验装置,开展橡胶材料单轴拉伸实验;其次,结合Exp-ln超弹性本构模型和广义黏弹性方法,建立了橡胶材料黏超弹本构模型;再次,推导本构模型三维增量格式,编写了用户子程序(VUMAT),验证了本构模型的一维和三维有效性;最后,建立橡胶底座冲击附加载荷计算数值模型,并将冲击附加载荷实验与数值仿真进行对比验证。结果表明:单轴拉伸实验与数值解吻合较好,冲击附加载荷实验值与仿真值误差约为7%,验证了黏超弹本构模型的正确性。
A visco-hyperelastic constitutive model was proposed to describe mechanical responses of rubber material under different strain rates. Firstly,the uniaxial tensile tests for rubber material were conducted with Instron testing machines and SHTB testing devices. Secondly,combined with Exp-ln hyperelastic constitutive model and the generalized viscoelastic method,the visco-hyperelastic constitutive model for rubber material was built. Thirdly,the three-dimensional incremental format of the visco-hyperelastic constitutive model was deduced,the user subroutine VUMAT was written,the one-dimensional effectiveness and three-dimensional one were verified. Finally,the impact additional load numerical simulation model of a rubber base was established,the results of impact additional load tests were compared with those of the numerical simulation. The results showed that the numerical results agree well with the uniaxial tensile test data,the error between the impact additional load test value and the simulation one is approximately 7%,the correctness of the visco-hyperelastic constitutive model is verified.
A visco-hyperelastic constitutive model was proposed to describe mechanical responses of rubber material under different strain rates. Firstly,the uniaxial tensile tests for rubber material were conducted with Instron testing machines and SHTB testing devices. Secondly,combined with Exp-ln hyperelastic constitutive model and the generalized viscoelastic method,the visco-hyperelastic constitutive model for rubber material was built. Thirdly,the three-dimensional incremental format of the visco-hyperelastic constitutive model was deduced,the user subroutine VUMAT was written,the one-dimensional effectiveness and three-dimensional one were verified. Finally,the impact additional load numerical simulation model of a rubber base was established,the results of impact additional load tests were compared with those of the numerical simulation. The results showed that the numerical results agree well with the uniaxial tensile test data,the error between the impact additional load test value and the simulation one is approximately 7%,the correctness of the visco-hyperelastic constitutive model is verified.
引文
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[2]Drozdov A D,de C Christiansen J.Consti-tutive equations in finite elasticity of swollen elastomers[J].International Journal of Solids and Structures,2013,50(9):1494-1504.
[3]Kovalev V A,Radaev Y N.Three-dimensional constitutive relations of ideal plasticity and the flow on the coulombtrescaprism edge[J].Mechanics of Solids,2010,45(2):295-308.
[4]Yang L M,Shim V P W,Lim C T.A visco-hyperelastic approach to modeling the constitutive behavior of rubber[J].International Journal of Impact Engineering,2000,24(6):545-560.
[5]Yang L M,Shim V P W.A visco-hyperelastic constitutive description of elastomeric foam[J].International Journal of Impact Engineering,2004,30(8):1099-1110.
[6]周相荣,王强,王宝珍,等.一种基于Yeoh函数的非线性黏超弹本构模型及其在冲击仿真中的应用[J].振动与冲击,2007,26(5):33-37.ZHOU Xinag-rong,WANG Qiang,WANG Bao-zhen,et al.A nonlinear visco-hyperelastic constitutive model based on Yeoh strain energy function with its application to impact simulation[J].Journal of Vibration and Shock,2007,26(5):33-37.
[7]Pouriayevali H,Guo Y B,Shim V P W.A viscohyperelastic constitutive description of elastomer behavior at high strain rates[J].Procedia Engineering,2011,10:2280-2285.
[8]常新龙,赖建伟,张晓军,等.HTPB推进剂高应变率黏弹性本构模型研究[J].推进技术,2014,35(1):123-127.CHANG Xin-long,LAI Jian-wei,ZHANG Xiao-jun,et al.High strain rate visco-elastic constitutive model for HTPB propellant[J].Journal of Propulsion Technology,2014,35(1):123-127.
[9]Chen X H.Nonlinear electro-thermo-visco-elasticity[J].Acta Mechanica,2010,211(1/2):49-59.
[10]胡少青,鞠玉涛,常武军,等.NEPE固体推进剂粘一超弹性本构模型研究[J].兵工学报,2013,34(2):168-173.HU Shao-qin,JU Yu-tao,CHANG Wu-jun,et al.A viscohyperelastic constitutive behaviour of NEPE propellant[J].Acta Armamentar II,2013,34(2):168-173.
[11]Khajehsaeid H,Arghavani J,Naghdabadi R.A hyperelastic constitutive model for rubber-like materials[J].European Journal of Mech-anics/A Solids,2013,38:144-151.
[12]Gamonpilas C,Mc Cuiston R.A nonlinear viscoelastic material constitutive model for polyurea[J].Polymer,2012,53(17):3655-3658.
[13]Li Shao-hua,Yang shao-pu,Chen Li-qun,et al.A nonlinear vehicle-road coupled model for dynamics research[J].Journal of Computational and Nonlinear Dynamics,2013,8(2):1-14.
[14]Anani Y,Alizadeh Y.Visco-hyperelastic consti-tutive law for modeling of foam’s behavior[J].Materials and Design,2011,32:2940-2948.
[15]张伟,魏刚,肖新科,等.2A12铝合金本构关系和失效模型[J].兵工学报,2013,34(3):276-282.ZHANG Wei,WEI Gang,XIAO Xin-ke,et al.Constitutive relation and fracture criterion of 2A12 aluminum alloy[J].Acta Armamentar II,2013,34(3):276-282.
[16]Kadlowec J,Wineman A,Hulbert G.Elastomer bushing response:experiments and finite element modeling[J].Acta Mechanica,2003,163(1/2):25-38.