USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS

Zheng Yuxuan; Chen Liang; Zhou Fenghua; Wang Lili

doi:10.6052/0459-1879-14-002

Volume 46 Issue 6

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Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2014 > 46(6): 843-852

Zheng Yuxuan, Chen Liang, Zhou Fenghua, Wang Lili. USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 843-852. doi: 10.6052/0459-1879-14-002

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Zheng Yuxuan, Chen Liang, Zhou Fenghua, Wang Lili. USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(6): 843-852. doi: 10.6052/0459-1879-14-002

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USING LAPLACE TRANSFORM TO SOLVE THE VISCOELASTIC WAVE PROBLEMS IN THE SHPB EXPERIMENTS

doi: 10.6052/0459-1879-14-002

MOE Key Laboratory of Impact and Safety Engineering, Ningbo University, Ningbo 315211, China

Funds: The project was supported by the National Natural Science Foundation of China (11272163, 11390361).

Received Date: 2013-12-31
Rev Recd Date: 2014-02-28
Publish Date: 2014-11-18

Abstract

Abstract

In relation to the dynamic tests of materials, the approach to solve the viscoelastic wave propagations in split Hopkinson pressure bar (SHPB) tests was summarized. By conducting Laplace transform, the governing partial differential equations were transformed to ordinary differential equations for the image functions, which were solved analytically with suitable boundary equations. Inversely transforming these image functions gives the results of the stress, velocity, and strain in the bar. A wave problem are analyzed to evaluate the internal stress distributions in a viscoelastic specimen occurred in SHPB tests. The problem was solved numerically by way of numerical inverse Laplace transform. A special case when the specimen is pure elastic was solved analytically, giving the exact solution to the problem of elastic wave propagation in a sandwich elastic media.
- viscoelasticity wave,
- SHPB,
- analytical solution,
- Laplace transform,
- numerical inverse transform

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References(17)

References

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