Abstract
The constitutive equations that have been developed for the dynamic behavior of materials presuppose the existence of a reference “static” yield criterion. An alternative formulation motivated by the work on dislocation dynamics considers the total deformation to consist of elastic and plastic components throughout the deformation history. This procedure permits the consideration of large deformations (finite strains) in a direct manner. The present paper outlines an elastic-viscoplastic theory based on this approach and includes numerical results for an internally pressurized thick walled sphere.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
J. F. Bell, “Single, Femperature Dependent Stress-Strain law For the Dynamic Plastic Deformation of Annealed FCC Metals,” J. Appl. Plus., 34, 131 (1963).
J. F. Bell. “Geneialized Large Deformation Behavior for FCC Solids,” Phil. Mag., 11, 1135 (1965).
A. Rosen and S. R. Bodner, “‘I’ he Inlluence of Strain Rate and Strain Age ing on the Flow Stress of Commercially-Pure Aluminum,” J. Mech. Phvs. Solids, 15, 17 (1967).
S. R. Bodner and A. Rosen, “Discontinuous Yielding of Commercially-Pure Aluminum,” J. Mech. Phys. Solids, 15, 63 (1967).
M. J. Manjoine, “Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel,” Frans. ASMF, 66, A211 (1944).
L. E. Malvern, “Plastic Wave Propagation in a Bar of Material Exhibiting a Strain Rate Effect,” Quart. Appl. Math., 8, 405 (1950).
L. E. Malvern, “The Propagation of Longitudinal Waves of Plastic Deformation in a Bar of Material Exhibiting a Strain Rate Effect,” J. Appl. Mech., 18, 203 (1951).
S. R. Bodner and P. S. Symonds, “Experimental and Theoretical Investigation of the Plastic Deformation of Cantilever Beams Subjected to Impulsive Loading,” J. Appl. Mech., 29, 719 (1962).
S. R. Bodner and W. G. Speirs, “Dynamic Plasticity Experiments on Aluminum Cantilever Beams at Elevated Temperature,” J. Mech. Phys. Solids, 77, 65 (1963).
J. Lubliner. “A Generalized Theory of Strain Rate Dependent Plastic Wave Propagation in Bars,” J. Mech. Phys. Solids, 12, 59 (1964).
P. Perzyna, “The Constitutive Equations for Rate Sensitive Plastic Materials,” Quart. Appl. Math., 20, 321 (1963).
See: W. Prager, Introduction to Mechanics of Continua, Ginn and Co., Boston, Mass., 136 (1961).
P. Perzyna, “The Study of the Dynamic Behavior of Rate Sensitive Plastic Materials,” Arch. Mech. Stos., 15, 113 (1963).
U. S. Lindholm, “Dynamic Deformation of Metals,” in Behavior of Materials Under Dynamic Loading, ed. by N. J. Huffington, Jr., ASME, New York (1965).
P. Perzyna and W. Wojno, “On the Constitutive Equations of Elastic/Viscoplastic Materials at Finite Strain,” Arch. Mech. Stos., 18, 85 (1966).
W. G. Johnston and J. J. Gilman, “Dislocation Velocities, Dislocation Densities, and Plastic Flow in Lithium Fluoride Crystals,” J. Appl. Phys., 30, 129 (1959).
W. G. Johnston, “Yield Points and Delay Times in Single Crystals,” J. Appl. Phys., 33, 2716 (1962).
G. T. Hahn, “A Model for Yielding with Special Reference to the Yield Point Phenomena of Iron and Related BCC Metals,” Acta Met., 10, 727 (1962).
J. J. Gilman, “Dislocation Mobility in Crystals,” J. Appl. Phys., 36, 3195 (1965).
S. R. Bodner, “The Mechanics of Repeated Discontinuous Yielding of Metals,” Mat. Science and Engin. 2, 213 (1967).
Y. Partom and S. R. Bodner, “Large Deformations of an Elastic-Visco-plastic Sphere” (in preparation).
Y. Partom, “The Dilatational and Distortional Partition of the Energy Function in Finite Strain,” Israel J. Tech., 4, 218 (1966).
G. T. Hahn, C. N. Reid, and A. Gilbert, “Dislocation Dynamics of Yielding and Fracture,” Proc. of Symposium on the Role of Substructure in the Mechanical Behavior of Metals, Report No. ASD-TR-63-324, U.S. Air Force Systems Command, 253 (1963).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1968 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Bodner, S.R. (1968). Constitutive Equations for Dynamic Material Behavior. In: Lindholm, U.S. (eds) Mechanical Behavior of Materials under Dynamic Loads. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87445-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-87445-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-87447-5
Online ISBN: 978-3-642-87445-1
eBook Packages: Springer Book Archive