One-Dimensional Interaction of a Cylindrical Unloading wave with a Moving Elastic Plastic Boundary

2018 ◽  
Keyword(s):  
One Dimensional ◽  
Elastic Plastic ◽  
Dimensional Interaction ◽  
Unloading Wave

Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 782-786 ◽  
Author(s):  
R. J. Clifton
Keyword(s):  
Wave Propagation ◽  
Time Derivative ◽  
Plastic Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Simple Waves ◽  
Thin Walled Tube ◽  
Loading And Unloading ◽  
All Speeds

Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

Wave Propagation in One-Dimensional Structure of Periodic Inelasticity Composites

2011 ◽  
Author(s):  
Helio Aparecido Navarro ◽  
Meire Pereira de Souza Braun
Keyword(s):  
Wave Propagation ◽  
Vibration Suppression ◽  
Stop Band ◽  
Dimensional Structure ◽  
Material Models ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Structural Problems ◽  
Plastic Damage ◽  
Non Linear

This study involves the analysis of elastic-plastic-damage dynamics of one-dimensional structures comprising of periodic materials. These structures are composed by multilayer unit cells with different materials. The dynamical characteristics of the composite material present distinct frequency ranges where wave propagation is blocked. The steady-state forced analyses are conducted on a structure constructed from a periodic inelasticity material. The material models have a linear dependence for elasticity problems and non-linear for elastoplasticity-damage problems. This paper discusses the pass and stop-band dispersive behavior of material models on temporal and spatial domains. For this purpose, some structural problems are composed of periodic and damping materials for analysis of vibration suppression have been simulated. This work brings a formulation of Galerkin method for one-dimensional elastic-plastic-damage problems. A time-stepping algorithm for non-linear dynamics is also presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spatial discretization the standard finite element method is used. The procedure proposed in this work can be extended to multidimensional problems, analysis of strain localization, and for others material models.

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