Uniform investigation of hydraulic fracturing propagation regimes in the plane strain model

2014 ◽  
Vol 39 (5) ◽  
pp. 507-523 ◽  
Author(s):  
J.Q. Bao ◽  
E. Fathi ◽  
S. Ameri
Keyword(s):  
Hydraulic Fracturing ◽  
Plane Strain ◽  
Strain Model ◽  
Plane Strain Model

A New Embedded-Zone Method on Computation of the Transverse Elastic Properties of Fiber-Reinforced Composites

2005 ◽  
Author(s):  
Xiaochun Wang
Keyword(s):  
Plane Strain ◽  
Elastic Properties ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
Zone Method ◽  
Two Dimension ◽  
The Matrix ◽  
Strain Model ◽  
Plane Strain Model

There are many methods on computation of transverse elastic properties of unidirectional fiber-reinforced composites when using the finite element method, such as three-dimension model, two-dimension plane strain model, unit cell model, etc[1]. But unit cell models could be used only when the fibers are arrayed regularly. The computations of three- and two-dimension plane strain models are tremendous when many fine fibers are spread randomly in the matrix so that the properties of block of composite must be computed. The paper proposes a new embedded-zone method to compute the transverse elastic properties for a block of fiber-reinforced composites containing a great amount of fibers embedded in the matrix stochastically while using very little computational work compared with three- and two-dimension plane strain model. The transverse elastic modulus and shear modulus of unidirectional fiber-reinforced composites are computed.

Thermal Stresses in Layered Electrical Assemblies Bonded With Solder

1991 ◽  
Vol 113 (4) ◽  
pp. 350-354 ◽  
Author(s):  
H. S. Morgan
Keyword(s):  
Residual Stresses ◽  
Plane Strain ◽  
3D Model ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Creep Models ◽  
Strain Model ◽  
Maximum Stresses ◽  
Generalized Plane Strain ◽  
Plane Strain Model

Thermal stresses in a layered electrical assembly joined with solder are computed with plane strain, generalized plane strain, and three-dimensional (3D) finite element models to assess the accuracy of the two-dimensional (2D) modeling assumptions. Cases in which the solder is treated as an elastic and as a creeping material are considered. Comparison of the various solutions shows that, away from the corners, the generalized plane strain model produces residual stresses that are identical to those computed with the 3D model. Although the generalized plane strain model cannot capture corner stresses, the maximum stresses computed with this 2D model are, for the mesh discretization used, within 12 percent of the corner stresses computed with the 3D model when the solder is modeled elastically and within 5 percent when the solder is modeled as a creeping material. Plane strain is not a valid assumption for predicting thermal stresses, especially when creep of the solder is modeled. The effect of cooling rate on the residual stresses computed with creep models is illustrated.

Multiple Diffractions of Elastic Waves by a Rigid Rectangular Foundation: Plane-Strain Model

1976 ◽  
Vol 43 (2) ◽  
pp. 291-294 ◽  
Author(s):  
M. Dravinski ◽  
S. A. Thau
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Elastic Waves ◽  
Equation Of Motion ◽  
Elastic Half Space ◽  
Strain Type ◽  
Time Required ◽  
Strain Model ◽  
Rectangular Foundation ◽  
Plane Strain Model

A rigid rectangular foundation embedded in an elastic half space moves in a direction perpendicular to the surface of the half space, Fig. 1. The model under consideration is of the plane-strain type. By application of the Laplace, Fourier, and Kontorovich-Lebedev (K-L) transforms, the equation of motion for the foundation is derived. The transient response of the foundation is exact during the period of time required for a longitudinal wave to traverse the base of the foundation twice. Thus the process of multiple diffractions at the corners of the foundation is taken into account.

Study on the Influence of Pit Excavation on the Stability of Underground Openings Using Different Models

2013 ◽  
Vol 353-356 ◽  
pp. 1466-1469
Author(s):  
Ya Xin Yang ◽  
Guo Jian Shao ◽  
Jing Fu Yu ◽  
Guang Yuan Chen
Keyword(s):  
Finite Element Method ◽  
Plane Strain ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Dimensional Plane ◽  
Underground Openings ◽  
The Stability ◽  
D Model ◽  
Strain Model ◽  
Plane Strain Model

Simplified plane strain model and 3-D model were used to research the influence of pit excavation on the stability of underground openings using the finite element method (FEM). Conclusion from the 3-D FEM study is that the central region of the pit will have a large springback deformation and the openings will also float up at the same time because of large ranges of pit excavation. When using the simplified two-dimensional plane strain model for the analysis of this problem, the size of the excavation region leads directly to two completely inconsistent results. If the excavation region was wider than the openings the springback deformation would be obtained, while the settlement would be obtained if the opening was wider than the excavation region. Therefore the two-dimensional plane strain model is not proper for the analysis of the stability of the openings under this condition.

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