Fitting Research on the Relaxation Function of Shear Modulus for Viscoelastic Materials

Abstract

Abstract: The characteristic parameters of viscoelastic physical model must be provided for the finite element analysis of viscoelastic materials. A numerical fitting method was used to derive the relationship of the generalized Maxwell model and the normalized experimental curve in terms of a model simplified for the viscoelastic material-costal cartilage, realize the fitting of experimental curve with the generalized Maxwell model, and receive the Maxwell model parameters of costal cartilage for viscoelastic finite element analysis. The simulation shows that the curve fitting degree is high.

Key words: solid mechanics, viscoelastic, Maxwell model, relaxation function of shear modulus, parameter fitting, finite element

CLC Number:

O345

WEI Yan-bin, SHI Yi-kai, LIU Peng. Fitting Research on the Relaxation Function of Shear Modulus for Viscoelastic Materials[J]. Acta Armamentarii, 2010, 31(10): 1409-1412.

References

［1］ Thomas F Soules. Finite-element calculation of stresses in glass parts undergoing viscous relaxation［J］. Am Ceram Soc,1999, 70(2):90-95.
［2］ George W Scherer. Viscoelastic-elastic composites: Ⅰ general theory［J］. Am Ceram Soc, 2002, 65(7):352-360.
［3］ Sakaguchi S. Viscosity of silica core optical fiber［J］. Journal of Non-Crystalline Solids,1999,224:232-237.
［4］ Follstaedt D M, Knapp J A, Myers S M. Mechanical properties of ion-implanted amorphous silicon［J］. Journal of Materials Research, 2004, 19(1):338-346.
［5］ Brendan E K, Jack L L. A model of fracture testing of soft viscoelastic tissues［J］. Journal of Biomechanics, 2003, 36(1):605-608.
［6］ Hsuch C H. Mathematical model of viscosity measurements for viscoelastic solids［J］. J Am Ceram Soc, 1986, 69(3):48-49.
［7］帅词俊,段吉安,王炯. 关于黏弹性材料的广义Maxwell模型［J］. 力学学报, 2006, 38(4):565-569.
SHUAI Ci-jun, DUAN Ji-an, WANG Jiong. A method of establishing generalized Maxwell model for viscoelastic material［J］. Chinese Journal of Theoretical and Applied Mechanics, 2006, 38(4):565-569.(in Chinese)
［8］帅词俊,段吉安,王炯. 数值分析中粘弹材料剪切模量松弛函数的拟合方法［J］. 机械强度, 2005, 27(4):522-525.
SHUAI Ci-jun, DUAN Ji-an, WANG Jiong. Fitting method of shear modulus relaxation function for viscoelastic materials in numerical analysis［J］. Journal of Mechanical Strength, 2005, 27(4):522-525.(in Chinese)
［9］帅词俊,段吉安,王炯,等. 经验应力松弛模量与Maxwell模量的转化计算方法［J］. 机械科学与技术, 2005, 24(5):628-630.
SHUAI Ci-jun, DUAN Ji-an, WANG Jiong, et al. A computational method for experimental stress relaxation modulus transited to Maxwell modulus［J］. Mechanical Science and Technology, 2005, 24(5):628-630.(in Chinese)
［10］郭碧云,李晓阳,曾衍钧,等. 肋软骨生物力学性能研究［J］. 中国生物医学工程学报,2007,26 (2) : 270-275.
GUO Bi-yun, LI Xiao-yang, ZENG Yan-jun, et al. Study on biomechanical characteristics of costal cartilage［J］. Chinese Journal of Biomedical Engineering,2007,26 (2) : 270-275. (in Chinese)
［11］蔡峨. 粘弹性力学基础［M］. 北京:北京航空航天大学出版社,1989:112-132.
CAI E. Viscoelastic mechanics basis［M］. Beijing: Beijing University of Aeronautics and Astronautic Press,1989:112-132. (in Chinese)

[1]	SUN Tongsheng, ZHU Junyao, YU Cungui, YANG Wenchao, XU Qiang. Prediction of Moisture Absorption-creep Coupling Behavior of Box-type Composite Directors for Multiple Launch Rocket System under Long-term Stacking Storage [J]. Acta Armamentarii, 2021, 42(3): 487-498.
[2]	WANG Zhiqian, MAO Baoquan, ZHU Rui, BAI Xianghua, HAN Xiaoping. Fractional Maxwell Model for Oscillating Flow of a Viscoelastic Elastomer Shock Absorber [J]. Acta Armamentarii, 2020, 41(5): 984-995.
[3]	WANG Zhiqian, MAO Baoquan, ZHU Rui, YANG Yuying, HAN Xiaoping. Test Study of Viscoelastic Elastomer Damper for Remote Weapon Station [J]. Acta Armamentarii, 2020, 41(2): 209-221.
[4]	WANG Zhiqian, MAO Baoquan, FENG Shuai, YANG Yuying, ZHU Rui. Fractional Maxwell Model of Start-up Flow for a Viscoelastic Elastomer Shock Absorber [J]. Acta Armamentarii, 2019, 40(10): 1977-1986.
[5]	XU Xiao, GAO Shi-qiao, NIU Shao-hua, SHEN Li, LIU Hai-peng, OU Zhuo-cheng. Dynamic Analysis of Projectile-borne Electronic Devices under Impact Loading [J]. Acta Armamentarii, 2017, 38(7): 1289-1300.
[6]	GAO Jun-qiang, TANG Xia-qing, HUANG Xiang-yuan, CHENG Xu-wei. FEA Method for Analysis of SINS Error Caused by Vibration Isolation System [J]. Acta Armamentarii, 2016, 37(9): 1570-1577.
[7]	DAI Yong, QIAN Lin-fang, WU Xiao-jin, XU Ya-dong. Analysis about Thermal-structure Coupling Effect of High Firing Rate Automatic Mechanism of a Gun [J]. Acta Armamentarii, 2016, 37(9): 1738-1743.
[8]	XU Xiao, FAN Li-xia, WANG Ya-ping, DONG Xiao-bin. Trans-scale Polycrystalline Finite Element Simulation of Radial Forging Process for Barrel and Prediction of Texture [J]. Acta Armamentarii, 2016, 37(7): 1180-1186.
[9]	ZHOU Jin-yu, XIE Li-yang, ZHU Fu-xian, HAN Wen-qin. Meso-scale Probabilistic Model of Fatigue Crack Nucleation Life [J]. Acta Armamentarii, 2016, 37(2): 307-316.
[10]	DING Chuan-jun, ZHANG Xiang-yan, LIU Ning. A Parametric Modeling Method for Gun Barrel and a Meshing Generation Strategy for Worn Barrel [J]. Acta Armamentarii, 2016, 37(12): 2212-2219.
[11]	CHEN Pan， QI Qiong-fang. Coupled Motion Analysis of Finite Ribbed Plate Based on Traveling Wave Approach [J]. Acta Armamentarii, 2016, 37(11): 2128-2135.
[12]	XU Yao-feng， DING Hong-min， XU Jian， NING Bian-fang. Numerical Analysis of Influence of Rifling Structure of Large Caliber Gun on Moving of Projectile with Sliding Driving Band in Bore [J]. Acta Armamentarii, 2016, 37(11): 2148-2156.
[13]	LIN Qing-hua， LI Bao-ming. Measurement and Numerical Simulation of Transient Electromagnetic Field in Railgun [J]. Acta Armamentarii, 2016, 37(10): 1788-1794.
[14]	DENG Wei, MAO Bao-quan, FENG Shuai, LI Cheng. Optimization of Muzzle Disturbance of Overhead Weapon Station Based on Kriging Model [J]. Acta Armamentarii, 2016, 37(10): 1795-1802.
[15]	SUN Bao, SUN Da-gang, LI Zhan-long, YAN Bi-juan, WANG Jun. Modified Modal Strain Energy Method for Analysis of Modal Loss Factors of Viscoelastic Structure [J]. Acta Armamentarii, 2016, 37(1): 155-164.