A two-dimensional source function for a dynamic brittle bilateral tensile crack

1970 ◽  
Vol 60 (4) ◽  
pp. 1209-1219 ◽  
Author(s):  
Merle E. Hanson ◽  
Allan R. Sanford
Keyword(s):  
Source Function ◽  
Near Field ◽  
Tensile Fracture ◽  
Two Dimensional ◽  
Tensile Crack ◽  
Elastic Continuum ◽  
Fracture Geometry ◽  
Velocity Function ◽  
Final Fracture ◽  
Fracture Velocity

abstract A numerical technic is used to simulate the two-dimensional elastic dynamic characteristics of a bilateral tensile fracture that accelerates, propagates and stops in an elastic continuum. The fracture-velocity function is specified for the calculation. Particle motion in the near field about the final fracture geometry is the result. Motion parallel to the fracture amounts to as much as 50 per cent of the perpendicular motion near the crack. The relaxation begins to occur after the fracture stops and the dynamic elastic radiation from both tips crosses the material.

scholarly journals Near-field observations of light confinement in a two dimensional lithium niobate photonic crystal cavity

2011 ◽  
Vol 110 (7) ◽  
pp. 074318 ◽  
Author(s):  
Jean Dahdah ◽  
Maria Pilar-Bernal ◽  
Nadège Courjal ◽  
Gwenn Ulliac ◽  
Fadi Baida
Keyword(s):  
Photonic Crystal ◽  
Lithium Niobate ◽  
Near Field ◽  
Field Observations ◽  
Two Dimensional ◽  
Photonic Crystal Cavity ◽  
Light Confinement

scholarly journals Buckling of Continuously Supported Beams

1973 ◽  
Vol 40 (2) ◽  
pp. 546-552 ◽  
Author(s):  
G. K. N. Murthy
Keyword(s):  
Two Dimensional ◽  
Elastic Continuum ◽  
Buckling Loads

The buckling of infinite beams continuously supported by a semi-infinite elastic continuum is investigated. The buckling loads were determined when the beam rests on a two-dimensional elastic continuum and also when the foundation extends beyond the width of the beam. The effect of the outside foundation is shown by comparing the obtained buckling loads.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

Tin diselenide van der Waals materials as new candidates for mid-infrared waveguide chips

Nanoscale ◽  
2019 ◽  
Vol 11 (30) ◽  
pp. 14113-14117 ◽  
Author(s):  
Mengfei Xue ◽  
Qi Zheng ◽  
Runkun Chen ◽  
Lihong Bao ◽  
Shixuan Du ◽  
...  
Keyword(s):  
Near Field ◽  
Van Der Waals ◽  
Building Blocks ◽  
Two Dimensional ◽  
Mid Infrared ◽  
Near Field Imaging ◽  
Van Der Waals Materials ◽  
Field Imaging

Near-field imaging of mid-infrared waveguide in SnSe2 slabs promotes two-dimensional van der Waals materials as building blocks for integrated MIR chips.

Unique Fall Off Signatures for Stage Fracture Characterization, Actual Field Cases

2021 ◽  
Author(s):  
Ahmed Farid Ibrahim ◽  
Mazher Ibrahim ◽  
Matt Sinkey ◽  
Thomas Johnston ◽  
Wes Johnson
Keyword(s):  
Flow Regime ◽  
Surface Area ◽  
Fiber Optics ◽  
In Situ Stress ◽  
Tensile Fracture ◽  
Finite Conductivity ◽  
Well Performance ◽  
Fracture Geometry ◽  
Fracture Conductivity ◽  
Diagnostic Plots

Abstract Multistage hydraulic fracturing is the common stimulation technique for shale formations. The treatment design, formation in-situ stress, and reservoir heterogeneity govern the fracture network propagation. Different techniques have been used to evaluate the fracture geometry and the completion efficiency including Chemical Tracers, Microseismic, Fiber Optics, and Production Logs. Most of these methods are post-fracture as well as time and cost intensive processes. The current study presents the use of fall-off data during and after stage fracturing to characterize producing surface area, permeability, and fracture conductivity. Shut-in data (15-30 minutes) was collected after each stage was completed. The fall-off data was processed first to remove the noise and water hammer effects. Log-Log derivative diagnostic plots were used to define the flow regime and the data were then matched with an analytical model to calculate producing surface area, permeability, and fracture conductivity. Diagnostic plots showed a unique signature of flow regimes. A long period of a spherical flow regime with negative half-slope was observed as an indication for limited entry flow either vertically or horizontally. A positive half-slope derivative represents a linear flow regime in an infinitely conductive tensile fracture. The quarter-slope derivative was observed in a bilinear flow regime that represents a finite conductivity fracture system. An extended radial flow regime was observed with zero slope derivative which represents a highly shear fractured network around the wellbore. For a long fall-off period, formation recharge may appear with a slope between unit and 1.5 slopes derivative, especially in over-pressured dry gas reservoirs. Analyzing fall-off data after stages are completed provides a free and real-time investigation method to estimate the fracture geometry and a measure of completion efficiency. Knowing the stage properties allows the reservoir engineer to build a simulation model to forecast the well performance and improve the well spacing.

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