Localization of plastic deformations as a result of wave interaction
Abstract
The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.
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References
[1] M.A. Dowaikh, RW. Ogden. Interfacial waves and deformations in pre-stressed elastic media. Proc. R. Soc. Lond., A433: 313- 328, 1991.[2] M.K. Duszek-Perzyna, P. Perzyna. Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids. Material Instabilities: Theory and Applications, AMD- Vol. 183 / MD- Vol. 50, ASME, 59- 85, 1994.
[3] M.K. Duszek-Perzyna, P. Perzyna. Acceleration waves in analysis of adiabatic shear band localization. In: J .L. Wegner, F.R Norwood, eds., Nonlinear Waves in Solids, Proc. IUTAM Symposium, August 15- 20, 1993, Victoria, Canada, pp. 128- 135. ASME, 1995.
[4] M.K. Duszek-Perzyna, P. Perzyna. Analysis of anisotropy and plastic spin effects on localization phenomena. Archive of Applied Mechanics, 68: 352-374, 1998.
[5] A. Glema, W. Kąkol, T. Łodygowski. Numerical modelling of adiabatic shear band formation in a twisting test. Engineering 7ransactions, 45(3-4): 419- 431, 1997.
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