Wave Propagation and Dynamic Response Analysis of Rate Dependent Materials
A method is proposed for describing the constitutive equation which is convenient to the experimental determination of characteristic parameters representing the mechanical behavior as well as the execution of numerical analysis. It is based on the mechanical model of generalized Voigt type comprising elastic, plastic, and rate-dependent viscoelastic components being connected in series. The relation for the general three dimensional case is derived first and the implications of relevant terms are discussed in detail by considering the uniaxial stress field. Numerical example of the application of the proposed method concerns with the solution of one demensional viscoelstic wave propagation by the finite difference and finite element methods.
KeywordsConstitutive Equation Elastic Wave Propagation Dynamic Response Analysis Consistent Mass Matrix Rate Dependent Material
Unable to display preview. Download preview PDF.
- 3.Campbell, J.D., Dynamic Plasticity of Metals, International Center for Mechanical Sciences, Udine/Italy, Courses and Lectures No. 46, 1970.Google Scholar
- 5.Yamada, Y., and Sakurai, T., “Basic Formulation and a computer Program for Inelastic Large Deformation Analysis,” Pressure Vessel Technology, Part I, ASME, 1977, pp. 341–352.Google Scholar
- 8.Yamada, Y., “Time Dependent Materials,” Computer Programs in Shock and Vibration, The Shock and Vibration Information Center, Naval Research Lab., Washington, D.C., 1975, pp. 173–188.Google Scholar
- 9.Yamada, Y., and Nagai, Y., “Analysis of One-Dimensional Stress Wave by the Finite Element Method,” Seisan-Kenkyu, Monthly J. of Institute of Industrial Science, Univ. of Tokyo, vol. 23, 1971, pp. 186–189.Google Scholar
- 11.Yamada, Y., and Sawada, T., “Analysis of Viscoelastic Wave Propagation with Particular Emphasis on Discontinuous Wave Front According to Finite Difference Method,” J. of Japan Society for Technology of Plasticity, vol. 10, 1969, pp. 141–148 (in Japanese).Google Scholar
- 12.Yamada, Y., and Sawada, T., “Analysis of One Dimensional Viscoelastic Wave Propagation with Discontinuities,”, ibid., vol. 11, 1970, pp. 724–734 (in Japanese).Google Scholar
- 13.Nakagawa, N., Kawai, R., and Sasaki, T., “Identification of Dynamic Properties and Wave Propagation in Viscoelastic Bars,” to be presented at this IUTAM symposium on High Velocity Deformation of Solids, August 24–27, 1977, Tokyo.Google Scholar
- 14.Kawata, K., Hashimoto, S., and Kurokawa, K., “Analysis of High Velocity Tension of Bars of Finite Length of bcc and fcc Metals with Their Own Constitutive Equations,” as above.Google Scholar
- 15.Yokoyama, T., and Tsuzuki, M., “Analysis of Elastic/ Viscoplastic Wave Propagation in a Bar by the Finite Element Method,” J. of Japan Society for Technology of Plasticity, vol. 18, 1977, pp. 11–15, (in Japanese).Google Scholar
- 16.Nakagiri, S., “Finite Element Analysis of the E-lastic-Plastic Wave Propagation in Metal Obeying the Strain-Rate Dependent Constitutive Equation,” Seisan-Kenkyu, Monthly J. of Institute of Industrial Science, Univ. of Tokyo, vol. 28, 1976, pp. 199–202 (in Japanese).Google Scholar
- 17.Fukuoka, H., “A Note on the Strength of the Combined Tension-Torsion Waves in Elastic-Plastic Tubes,” Symposium on Foundations of Plasticity, Noordhoff, 1973, pp. 317–325.Google Scholar