Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T16:41:27.968Z Has data issue: false hasContentIssue false
  • English
  • Français

Stress Wave Propagation for Nonlinear Viscoelastic Polymeric Materials at High Strain Rates

Published online by Cambridge University Press:  05 May 2011

Li-Lih Wang
Li-Lih Wang*
Affiliation:
Mechanics and Materials Science Research Center, Ningbo University, Ningbo, Zhejiang 315211, China
*
*Professor and Honorary Director
Get access

Abstract

Without knowing the dynamic constitutive relation of materials under high strain rates, no wave propagation can be correctly analyzed. A Series of experimental and theoretical investigation at high strain rates revealed that the nonlinear viscoelastic behavior of polymers and the related composites are well described by the Zhu-Wang-Tang (ZWT) nonlinear viscoelastic constitutive equation. The impulsive reponse of ZWT materials consists of a rate independent nonlinear elastic response and a high frequency linear viscoelastic response. The dispersion and attenuation of nonlinear viscoelastic waves mainly depend on the effective nonlinearity and the high frequency relaxation time θ2. An “effective influence distance” or “effective influence time” is defined to characterize the wave propagation range where θ2 dominates the impact relaxation process.

Keywords

Nonlinear viscoelasticityWave propagationConstitutive relationHigh strain rate.
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 177 - 183
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Kolsky, H., Stress Waves in Solids, Clarendon Press, Oxford (1953).Google Scholar
2Wang, Lili, Foundations of Stress Waves, National Defense Industry Press, Beijing (1985).Google Scholar
3Zukas, J. A., Nicholas, T., Swift, H., Greszczuk, L. B. and Curran, D. R., Impact Dynamics, John Wiley & Sons, Inc., New York (1982).Google Scholar
4Kolsky, H., “An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading,” Proc. Phys. Soc., B62, p. 676 (1949).CrossRefGoogle Scholar
5Tang, Zhiping, Tian, Lanqiao, Chu, Chao-Hsiang and Wang, Lili, “Mechanical Behavior of Epoxy Resin under High Strain Rates,” Proc. 2nd Nat. Conf. Explosive Mechanics, Yangzhou, China, pp. 4-1–12 (1981).Google Scholar
6Chu, Chao-Hsiang, Wang, Lili and Xu, Daben, “A Nonlinear Thermo-Viscoelastic Constitutive Equation for Thermoset Plastics at High Strain Rates,” Proc. Int. Conf. Nonlinear Mechanics, Shanghai, China, p. 92 (1985).Google Scholar
7Yang, Liming, Chu, Chao-Hsiang and Wang, Lili, “Effects of Short Glass Fiber Reinforcement on Nonlinear Viscoelastic Behavior of Poly- carbonate,” Explosion and Shock Waves, 6, p. 1 (1986).Google Scholar
8Zhu, Zhaoxiang, Xu, Daben and Wang, Lili, “Thermo-Viscoelastics Constitutive Equation and Time-Temperature Equivalence of Epoxy Resin at High Strain Rates,” Jour. Ningbo University (Natural Sci. & Engng. Edition), 1, p. 58 (1998).Google Scholar
9Wang, Lili, Zhu, Xixiong, Shi, Shaochu, Gan, Su and Bao, Hesheng, “An Impact Dynamics Investigation on Some Problems of Birds Striking the Windshields of High Speed Aircraft,” Chinese Jour. Aeronautics, 5, p. 205 (1992).Google Scholar
10Zhou, Fenghua, Wang, Lili and Hu, Shisheng, “A Damage Modified Nonlinear Viscoelastic Constitutive Relation and Failure Criterion of PMMA at High Strain Rates,” Explosion and Shock Waves, 12, p. 333 (1992).Google Scholar
11Wang, Lili and Yang, Liming, “A Class of Nonlinear Viscoelastic Constitutive Relation of Solid Polymeric Materials,” Progress in Impact Dynamics, Wang, Lili, Yu, Tongxi and Li, Yongchi, eds., The Press of China University of Science and Technology, Hefei, China, p. 88 (1992).Google Scholar
12Wang, Lili, Labibes, K., Azari, Z. and Pluvinage, G., “Generalization of Split Hopkinson Bar Technique to Use Viscoelastic Bars,” Int. Jour. Impact Engng. 15, p. 669 (1994).CrossRefGoogle Scholar
13Labebis, K., Wang, Lili and Pluvinage, G., “On Determining the Viscoelastic Constitutive Equation of Polymers at High Strain-Rates,” DYMAT Jour., 1, p. 135 (1994).Google Scholar
14Green, A. E. and Rivlin, R. S., “The Mechanics of Nonlinear Materials with Memory, Part 1,” Arch. Rat. Mech. Anal., 1, p. 1 (1957).CrossRefGoogle Scholar
15Coleman, B. D. and Noll, W., “An Approximation Theorem for Functionals with Applications in Continum Mechanics,” Arch. Rat. Mech. Anal., 6, p. 355 (1960).CrossRefGoogle Scholar
16Coleman, B. D. and Noll, W., “Foundations of Linear Viscoelasticity,” Rev. Mod. Phys., 33, p. 239 (1961).CrossRefGoogle Scholar
17Ting, T. C. T., Nonlinear Waves in Solids, China Press of Friendship, Beijing, China (1985).Google Scholar