Antiplane Eigenstrain Problem of an Elliptic Inclusion in a Two-Phase Anisotropic Medium

1985 ◽  
Vol 52 (1) ◽  
pp. 87-90 ◽  
Author(s):  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Anisotropic Medium ◽  
Strain Energy ◽  
Homogeneous Medium ◽  
Stress Singularity ◽  
Elliptic Inclusion ◽  
Two Phase ◽  
Line Force ◽  
Elastic Inhomogeneity ◽  
Inhomogeneity Factor ◽  
Force Concept

An antiplane eigenstrain problem of an elliptic inclusion in a two-phase anisotropic medium is analyzed based on the line-force concept. Explicit expressions for the stress field and strain energy are obtained under a given symmetry. The results are used to determine the stress singularity coefficient for a flat inclusion. When the tip of the inclusion is located at the interface boundary, the stress singularity coefficient S′ varies according to the formula S′ = (1 + K) S° where K is the elastic inhomogeneity factor and S° is the stress singularity coefficient for a homogeneous medium (K = 0).

Antiplane Eigenstrain Problem of an Elliptic Inclusion in an Anisotropic Half Space

1982 ◽  
Vol 49 (1) ◽  
pp. 52-54 ◽  
Author(s):  
R. A. Masumura ◽  
Y. T. Chou
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Energy ◽  
Infinite Medium ◽  
Elliptic Inclusion ◽  
Image Field ◽  
Line Force ◽  
Force Concept

The antiplane eigenstrain problem of an elliptic inclusion in an anisotropic semi-infinite medium is investigated. Expressions for the stresses and elastic energy have been developed using the line force concept and superposition of the image field. It is shown that in the presence of a free surface the stresses inside the inclusion are not constant. In addition, the elastic energy of the system is reduced as the inclusion approaches the free surface.

Antiplane Strain Problems of an Elliptic Inclusion in an Anisotropic Medium

1977 ◽  
Vol 44 (3) ◽  
pp. 437-441 ◽  
Author(s):  
H. C. Yang ◽  
Y. T. Chou
Keyword(s):  
Anisotropic Medium ◽  
Strain Energy ◽  
Elastic Field ◽  
Antiplane Strain ◽  
Elliptic Inclusion ◽  
Rigid Line ◽  
Uniform Stress Field ◽  
Elliptic Cavity ◽  
Stress Magnification ◽  
Elliptic Inhomogeneity

The antiplane strain problem of an elliptic inclusion in an anisotropic medium with one plane of symmetry is solved. Explicit expressions of compact form are obtained for the elastic field inside the inclusion, the stress at the boundary, and the strain energy of the system. The perturbation of an otherwise uniform stress field due to an elliptic inhomogeneity is studied, and explicit solutions are given for the extreme cases of an elliptic cavity and a rigid elliptic inhomogeneity. It is found that both the stress magnification at the edge of the inhomogeneity and the increase of strain energy depend only on the component P23A of the applied stress for an elongated cavity; and depend only on the component E13A of the applied strain for a rigid line inhomogeneity.

3D mapping of kinematic attributes in anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C159-C170 ◽  
Author(s):  
Yuriy Ivanov ◽  
Alexey Stovas
Keyword(s):  
Anisotropic Medium ◽  
Heterogeneous Media ◽  
Homogeneous Medium ◽  
Anisotropic Media ◽  
Transformation Matrix ◽  
3D Mapping ◽  
Slowness Surface ◽  
Point Correspondence ◽  
Geometric Spreading ◽  
Point To Point

Based on the rotation of a slowness surface in anisotropic media, we have derived a set of mapping operators that establishes a point-to-point correspondence for the traveltime and relative-geometric-spreading surfaces between these calculated in nonrotated and rotated media. The mapping approach allows one to efficiently obtain the aforementioned surfaces in a rotated anisotropic medium from precomputed surfaces in the nonrotated medium. The process consists of two steps: calculation of a necessary kinematic attribute in a nonrotated, e.g., orthorhombic (ORT), medium, and subsequent mapping of the obtained values to a transformed, e.g., rotated ORT, medium. The operators we obtained are applicable to anisotropic media of any type; they are 3D and are expressed through a general form of the transformation matrix. The mapping equations can be used to develop moveout and relative-geometric-spreading approximations in rotated anisotropic media from existing approximations in nonrotated media. Although our operators are derived in case of a homogeneous medium and for a one-way propagation only, we discuss their extension to vertically heterogeneous media and to reflected (and converted) waves.

The numerical simulation for a 3D two-phase anisotropic medium based on BISQ model

2008 ◽  
Vol 5 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Zhejiang Wang ◽  
Qiaodeng He ◽  
Deli Wang
Keyword(s):  
Numerical Simulation ◽  
Anisotropic Medium ◽  
Two Phase ◽  
Bisq Model

Line Force in a Two-Phase Orthotropic Medium

1982 ◽  
Vol 49 (1) ◽  
pp. 55-61 ◽  
Author(s):  
R. S. Wu ◽  
Y. T. Chou
Keyword(s):  
Free Surface ◽  
Elastic Field ◽  
Space Application ◽  
Orthotropic Medium ◽  
Method Of Images ◽  
Two Phase ◽  
Special Cases ◽  
Line Force ◽  
Technological Interest

Based on the generalized method of images, the elastic field of an in-plane line force acting in a two-phase orthotropic medium is analyzed. Several special cases of technological interest are deduced from the general solution, including the case of a line force applied on the free surface of a half space. Application of the results to the determination of the elastic field of an edge dislocation in a semi-infinite orthotropic medium is illustrated.

scholarly journals Scanning anisotropy parameters in complex media

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. U13-U22 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Anisotropic Medium ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
Transient Behavior ◽  
Complex Media ◽  
Linear Partial Differential Equations ◽  
Anisotropy Parameters ◽  
Axis Of Symmetry ◽  
Ti Media ◽  
Taylor’S Series

Parameter estimation in an inhomogeneous anisotropic medium offers many challenges; chief among them is the trade-off between inhomogeneity and anisotropy. It is especially hard to estimate the anisotropy anellipticity parameter η in complex media. Using perturbation theory and Taylor’s series, I have expanded the solutions of the anisotropic eikonal equation for transversely isotropic (TI) media with a vertical symmetry axis (VTI) in terms of the independent parameter η from a generally inhomogeneous elliptically anisotropic medium background. This new VTI traveltime solution is based on a set of precomputed perturbations extracted from solving linear partial differential equations. The traveltimes obtained from these equations serve as the coefficients of a Taylor-type expansion of the total traveltime in terms of η. Shanks transform is used to predict the transient behavior of the expansion and improve its accuracy using fewer terms. A homogeneous medium simplification of the expansion provides classical nonhyperbolic moveout descriptions of the traveltime that are more accurate than other recently derived approximations. In addition, this formulation provides a tool to scan for anisotropic parameters in a generally inhomogeneous medium background. A Marmousi test demonstrates the accuracy of this approximation. For a tilted axis of symmetry, the equations are still applicable with a slightly more complicated framework because the vertical velocity and δ are not readily available from the data.

scholarly journals Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

2013 ◽  
Vol 2013 ◽  
pp. 1-18
Author(s):  
Tie Jun ◽  
Sui Yun-kang
Keyword(s):  
Topology Optimization ◽  
Strain Energy ◽  
Stress Singularity ◽  
Continuous Mapping ◽  
Stress Constraints ◽  
Aggregation Function ◽  
Sensitivity Analyses ◽  
Stress Concentrations ◽  
Filter Function ◽  
Design Variables

This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditionalε-relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.

scholarly journals Torsional Strain Energy of Normal Concrete and SCC with Glass and Steel fibers

2020 ◽  
Vol 9 (1) ◽  
pp. 2300-2303
Keyword(s):  
Strain Energy ◽  
Glass Fibers ◽  
Minimum Energy ◽  
Steel Fibers ◽  
Analytical Models ◽  
Two Phase ◽  
Torsional Strain ◽  
Micro Cracks ◽  
Force Systems ◽  
Tensile Zone

Concrete is a two phase material with initial internal micro cracks before loading. When the load is applied on the specimen these internal cracks propagate and material fails after reaching its maximum allowable stress. There are different force systems like tensile, compressive, shear, torsion and combination of above. The strain energy is the energy which develops internally in the material to resist deformation because of application of external load. So if the minimum energy level is reached the deformation exceeds its plastic limit and cracks start propagating from tensile zone to compressive zone. Usually the torsional strain energy is studied to define the material characteristics for taking twisting and rotational effects in the member. A study is made regarding the torsional strain energy of ordinary and SCC with glass and steel fibers. Also a comparison is made for strain energy by experimental and analytical models. To give additional strength to the concrete, steel, and glass fibers are also added to SCC and their torsional strain energy was estimated.

Prediction of the path of unstable extension of internal and edge cracks

1980 ◽  
Vol 15 (4) ◽  
pp. 183-194 ◽  
Author(s):  
S K Maiti
Keyword(s):  
Energy Density ◽  
Tangential Stress ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Experimental Studies ◽  
Stress Singularity ◽  
Maximum Tangential Stress ◽  
Stress Criterion ◽  
Maximum Tangential Stress Criterion ◽  
Edge Cracks

The criteria of strain energy density and maximum tangential stress have been applied to the entire stress field existing just before the onset of instability to predict the path of extension of both internal and edge cracks. The stress analysis has been carried out by a finite-element scheme employing the quarter point square-root stress singularity elements. In the case of internal cracks, the unstable paths based on both the criteria are in good agreement with the results available in the literature. Theoretical and experimental studies on edge crack extensions during bar shearing of brittle materials have facilitated a comparison, and it appears that, although the maximum tangential stress criterion may be applicable, the strain energy density criterion is unsuitable for this case.

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