A Nonlinear Model for the Dynamics of Penetration Into Geological Targets

1982 ◽  
Vol 49 (1) ◽  
pp. 26-30 ◽  
Author(s):  
F. R. Norwood ◽  
M. P. Sears
Keyword(s):  
Shear Failure ◽  
Nonlinear Ordinary Differential Equation ◽  
Stress Wave Propagation ◽  
Normal Impact ◽  
Material Models ◽  
Shooting Technique ◽  
Failure Pressure ◽  
Asymptotic Values ◽  
Specific Material ◽  
General Material

A general theory is developed for predicting stress and force histories for normal impact and penetration of geological targets by conical-nosed projectiles. To account for general material properties, the target medium is described by arbitrary hydrostat and shear failure-pressure relations. Using the cylindrical cavity approximation, the penetration dynamics reduce to a problem of radially symmetric stress wave propagation involving a nonlinear, ordinary, differential equation in terms of similarity variables. This equation is solved numerically by a shooting technique which is initiated by asymptotic values at the wave front. Numerical results are given for the stresses on the penetrator nose for some specific material models.

scholarly journals Investigation on the Effects of Prefabricated Crack and Strain Rate on Uniaxial Compressive Properties of Frozen Silty Soil

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Dongdong Ma ◽  
Ezra Esanju Kaunda ◽  
Kun Huang
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Shear Failure ◽  
Rapid Change ◽  
Stress Wave Propagation ◽  
Peak Strain ◽  
Soil Specimen ◽  
Silty Soil ◽  
Fracturing Process ◽  
Deformation Properties

To investigate the uniaxial compressive strength and deformation properties of frozen silty soil with prefabricated crack under various strain rates, the static uniaxial compressive tests were conducted for frozen silty soil using three kinds of binder materials to select the suitable prefabricated crack manufacturing method. Afterward, the static and dynamic stress-strain curves of frozen silty soil with different prefabricated crack numbers were obtained based on static and splitting Hopkinson pressure bar (SHPB) tests. In addition, the high-speed camera was employed to record the fracturing process of frozen silty soil under impact loads. Results indicated that the frozen silty soil specimens with no binder showed higher static strength compared with other two binder materials (plaster and Vaseline). The strength growth rate of frozen silty soil showed three-stage (fast-slow-rapid) change characteristics. The peak strain of frozen silty soil under static loads scope was higher compared with that under dynamic loads, while its dynamic peak strain with various prefabricated crack numbers was remarkably rate-dependent. The absorbed energy density of frozen silty soil was subject to a negative (positive) relationship with the prefabricated crack numbers (strain rate). The dominated crack of intact frozen silty soil specimen finally presented Y-shaped shear failure. However, tensile cracks parallel to stress wave propagation direction were observed for the frozen silty soil specimen with prefabricated crack.

scholarly journals Effective stresses and shear failure pressure from in situ Biot's coefficient, Hejre Field, North Sea

2016 ◽  
Vol 65 (3) ◽  
pp. 808-822 ◽  
Author(s):  
J.B. Regel ◽  
I. Orozova-Bekkevold ◽  
K.A. Andreassen ◽  
N.C. Høegh van Gilse ◽  
I.L. Fabricius
Keyword(s):  
North Sea ◽  
Shear Failure ◽  
Failure Pressure ◽  
Effective Stresses ◽  
Biot’S Coefficient

Unsteady Flow of a Power–Law Fluid past a Shrinking Sheet with Mass Transfer

2012 ◽  
Vol 67 (1-2) ◽  
pp. 65-69 ◽  
Author(s):  
Nor Azizah Yacob ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Power Law ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Shrinking Sheet ◽  
Power Law Fluid ◽  
Suction Parameter ◽  
Shooting Technique ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Power Law Index

The unsteady two-dimensional boundary layer flow past a shrinking sheet in a non-Newtonian power-law fluid is investigated. The governing partial differential equations are transformed into a nonlinear ordinary differential equation using a similarity transformation before being solved numerically by the Runge-Kutta-Fehlberg method and the NAG Fortran library subroutine DO2HAF with shooting technique. The results obtained by both methods are in good agreement. It is found that dual solutions exist for a certain range of the unsteadiness parameter and the suction parameter. Moreover, by increasing the power-law index n, the skin friction coefficient is enhanced.

A Lattice Model for Stress Wave Propagation in Composite Materials

1973 ◽  
Vol 40 (1) ◽  
pp. 149-154 ◽  
Author(s):  
D. S. Drumheller ◽  
H. J. Sutherland
Keyword(s):  
Composite Materials ◽  
Wave Front ◽  
Lattice Model ◽  
Aluminum Matrix ◽  
Laminated Plates ◽  
Stress Wave Propagation ◽  
Wide Range ◽  
Precise Shape ◽  
The Matrix ◽  
Specific Material

Geometric dispersion, observed in a wide variety of composite materials, is believed to result mainly from the relatively periodic arrangement of the reinforcing elements in the matrix rather than from the precise shape of each reinforcing element. On the basis of this observation, a lattice model for composite materials which ignores the shape of the reinforcing elements but preserves their periodicity has been developed. For a wide range of engineering applications, this model can be used to predict the behavior of actual engineering composites. In the application of the lattice model to a specific material, consideration of the dispersive characteristics of the composite are set aside, initially, and the composite is treated as a nondispersive homogeneous mixture. The effective or average properties of the mixture are determined either by steady-wave analysis or appropriate experiments. A lattice is then formed by redistributing the mass within the mixture to form a periodic structure of laminated plates. This mass redistribution is carried out in a manner which yields a lattice with theoretical dispersive characteristics that match the measured dispersive characteristics of the composite. The model was applied to composites consisting of a regular array of tungsten fibers in an aluminum matrix and composed of 2.2 and 22.1 percent by volume of tungsten. Two flyer-plate experiments were performed in the plastic range of the composite. The agreement between experiment and calculation for the arrival time and rise time of the wave front and for the frequency of the ringing behind the wave front is good.

General material models

2008 ◽  
pp. 61-121
Author(s):  
Julie Dorsey ◽  
Holly Rushmeier ◽  
Françis Sillion
Keyword(s):  
Material Models ◽  
General Material

A Model to Estimate Forces on Conical Penetrators Into Dry Porous Rock

1981 ◽  
Vol 48 (1) ◽  
pp. 25-29 ◽  
Author(s):  
M. J. Forrestal ◽  
D. B. Longcope ◽  
F. R. Norwood
Keyword(s):  
Shear Failure ◽  
Equations Of Motion ◽  
Nonlinear Ordinary Differential Equation ◽  
Radial Coordinate ◽  
Porous Rock ◽  
Material Density ◽  
Cylindrical Cavity Expansion ◽  
Wide Range ◽  
Linear Shear ◽  
History Of

A model to predict the forces on conical-nosed penetrators for normal impact into dry rock targets is developed. The target medium is described by a linear hydrostat, a linear shear failure-pressure relation, and the material density. A cylindrical cavity expansion approximation to the target response permits one-dimensional wave propagation calculations in the radial coordinate. The equations of motion are reduced, via a similarity transformation, to a nonlinear ordinary differential equation. This equation is solved numerically by a shooting technique which employs an asymptotic expansion to the solution near the wave front. Results include stress wave profiles in the target and curves for the stress on the penetrator nose as a function of its velocity for a wide range of realistic target parameters. Finally, results from the theory are compared with the deceleration history of a penetrator in a field test and reasonable correlation is observed.

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