Approximate solution of dynamic bending problem for rigid plastic discs

1974 ◽  
Vol 10 (5) ◽  
pp. 481-486
Author(s):  
Yu. R. Lepik
Keyword(s):  
Approximate Solution ◽  
Rigid Plastic ◽  
Dynamic Bending

Modeling the dynamic bending of rigid-plastic fiber-reinforced laminated curvilinear doubly connected thin plates with free outer contour

2020 ◽  
pp. 108128652096254
Author(s):  
Tatiana Pavlovna Romanova
Keyword(s):  
Structural Model ◽  
Analytical Formula ◽  
Limit Load ◽  
Middle Surface ◽  
Plane Stress State ◽  
Thin Plates ◽  
Fiber Reinforced ◽  
Rigid Plastic ◽  
Dynamic Bending ◽  
Uniformly Distributed Loads

A theoretical model of the dynamic bending of rigid-plastic hybrid composite, arbitrary curvilinear doubly connected thin plates is developed. Inner contour of the plate is simply supported or clamped and outer one is free. The plates are on a viscous basis and under the action of uniformly distributed loads of explosive type. The plates are laminated and fibrous, with layers arranged symmetrically with respect to the middle surface. In each layer the reinforcing fibers, made of different materials, are located in directions parallel or normal to inner contour of plate. The structural model of the reinforced layer considering the plane stress state in fibers is used. The equations of the dynamic deformation of plate and simple analytical formula for the limit load are obtained. Numerical examples are given for a fiber-reinforced four-layered curvilinear plate with a supported hole in the form of ellipse and super-ellipse at the same total amount of reinforcement.

Modified split Hopkinson pressure bars for dynamic bending and shear tests

2006 ◽  
Vol 134 ◽  
pp. 725-730 ◽  
Author(s):  
A. Pignon ◽  
G. Mathieu ◽  
S. Richomme ◽  
J. M. Margot ◽  
F. Delvare
Keyword(s):  
Shear Tests ◽  
Split Hopkinson ◽  
Split Hopkinson Pressure Bars ◽  
Dynamic Bending

Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

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