Effective media: A forward modeling view

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2055-2062 ◽  
Author(s):  
Vladimir Grechka
Keyword(s):  
Layered Medium ◽  
Analytical Description ◽  
Complex Stress ◽  
Stress And Strain ◽  
Strain Fields ◽  
Stiffness Coefficients ◽  
Quantitative Estimates ◽  
Effective Media ◽  
Backus Averaging ◽  
Layered Solid

The existing effective media theories, such as Backus averaging, can be only used in media that possess certain characteristics regarding to concentration, shape, or geometry of their heterogeneities. These limitations originate from necessity of having analytical description of complex stress and strain fields that normally arise in microheterogeneous solids. The need for explicit solutions can be eliminated by computing the stresses and strains numerically. As a result, effective media can be in principle constructed for solids of arbitrary complexity. This simple idea is tested on two 2D models, where conventional analytical effective media theories are likely to break down. The first model is an isotropic layered solid with cracks that intersect the layer interfaces, the second is a layered medium containing random inclusions. In both cases, some differences are observed between the effective stiffness coefficients obtained numerically and those derived using the existing effective media theories. For instance, it is demonstrated that Backus averaging (improperly) applied to horizontal isotropic layers with random inclusions leads to biases in the calculated vertical velocities. Overall, the proposed technique enables us to establish the limits of applicability of conventional effective media theories. It also makes it possible to obtain quantitative estimates of the errors incurred because of violating certain assumptions of a given theory.

Three-Dimensional Finite Element Analysis of Subsurface Stress and Strain Fields Due to Sliding Contact on an Elastic-Plastic Layered Medium

1997 ◽  
Vol 119 (2) ◽  
pp. 332-341 ◽  
Author(s):  
E. R. Kral ◽  
K. Komvopoulos
Keyword(s):  
Finite Element Analysis ◽  
Material Properties ◽  
Layered Medium ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Element Analysis ◽  
Strain Fields ◽  
Contact Loads ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

A three-dimensional finite element analysis of a rigid sphere sliding on an elastic-plastic layered medium is presented. Results for the subsurface stress and strain fields are given for a perfectly adhering layer with an elastic modulus and yield stress both two and four times that of the substrate, and contact loads 100 and 200 times the initial yield load of the substrate material. Sliding is simulated to distances of approximately two to three times the initial contact radius. The sphere is modeled by contact elements, and the interface friction coefficient is assumed equal to 0.1 and 0.25. The effects of layer material properties, contact friction, and normal load on the sliding and residual stresses in the layer and the substrate are examined. The distributions of tensile stresses in the layered medium and shear stresses at the layer/substrate interface are presented and their significance for crack initiation and layer decohesion is discussed. Reyielding during unloading is also analyzed for different material properties and contact loads.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

The stress and strain fields in the neighbourhood of a notch in polyethylene

Polymer ◽  
1989 ◽  
Vol 30 (8) ◽  
pp. 1456-1461 ◽  
Author(s):  
Xue-qin Wang ◽  
Norman Brown
Keyword(s):  
Stress And Strain ◽  
Strain Fields

Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate

1983 ◽  
Vol 50 (4a) ◽  
pp. 789-794 ◽  
Author(s):  
K. C. Valanis ◽  
J. Fan
Keyword(s):  
Residual Stress ◽  
Numerical Scheme ◽  
External Loading ◽  
Stress And Strain ◽  
Elastoplastic Strain ◽  
Residual Stress Field ◽  
Progressive Change ◽  
Strain Fields ◽  
Cyclic Tension ◽  
Cyclic Elastoplastic Strain

In this paper we present an analytical cum-numerical scheme, based on endochronic plasticity and the finite element formalism. The scheme is used to calculate the stress and elastoplastic strain fields in a plate loaded cyclically in its own plane along its outer edges and bearing two symmetrically disposed edge notches. One most important result that stands out is that while the external loading conditions are symmetric and periodic, the histories of stress and strain at the notch tip are neither symmetric nor periodic in character. In cyclic tension ratcheting phenomena at the tip of the notches prevail and a progressive change of the residual stress field at the notch line is shown to occur.

scholarly journals Biomechanical Aspects of Closing Approaches in Postcarotid Endarterectomy

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Idit Avrahami ◽  
Dafna Raz ◽  
Oranit Bash
Keyword(s):  
Carotid Bifurcation ◽  
Stress And Strain ◽  
Surgery Complications ◽  
Artery Wall ◽  
Strain Fields ◽  
Structure Interaction ◽  
Cerebral Blood Supply ◽  
Patch Angioplasty ◽  
Alternative Approach ◽  
The Common

The carotid bifurcation tends to develop atherosclerotic stenoses which might interfere with cerebral blood supply. In cases of arterial blockage, the common clinical solution is to remove the plaque via carotid endarterectomy (CEA) surgery. Artery closure after surgery using primary closures along the cutting edge might lead to artery narrowing and restrict blood flow. An alternative approach is patch angioplasty which takes longer time and leads to more during-surgery complications. The present study uses numerical methods with fluid-structure interaction (FSI) to explore and compare the two solutions in terms of hemodynamics and stress and strain fields developed in the artery wall.

The influence of crack size on the ductile-brittle transition

1988 ◽  
Vol 415 (1848) ◽  
pp. 197-226 ◽  
Keyword(s):  
Boundary Layer ◽  
Fracture Toughness ◽  
Transition Temperature ◽  
Plane Strain ◽  
Crack Size ◽  
Specimen Geometry ◽  
External Loading ◽  
Stress And Strain ◽  
Strain Fields ◽  
Penny Shaped Crack

Simple criteria for brittle and ductile crack extension are applied to the stress and strain fields adjacent to the tip of a crack. They are applied at a specified distance from the crack tip, which should be related to the material’s microstructure. The basic approach is to examine each criterion and find which is satisfied first, as the external loading is increased; the predicted fracture is classified either brittle or ductile accordingly. The stress and strain fields depend upon temperature, principally through the variation of flow stress σ 0 with temperature and, to avoid excessive computation, a constitutive relation is constructed which allows stresses and strains both to be scaled in terms of σ 0 , so that major computations need to be done only at a reference temperature, for a range of applied loads. For any given crack configuration, the result of the calculation is a theoretical prediction of fracture toughness as a function of temperature. At low temperatures, the fracture toughness is low and rises rapidly with temperature, corresponding to satisfaction of the criterion for brittle failure. Above a transition temperature, T T , the ductile criterion is satisfied first, and the toughness variation thereafter falls slowly as temperature increases, corresponding to failure ‘on the upper shelf’. Both the absolute level of the toughness at a given temperature and the transition temperature T T are sensitive to crack size as well as specimen geometry. Although this is self-evident for cracks of microstructural dimensions, the striking feature of this work is the prediction that substantial sensitivity to size and geometry may well be displayed for cracks as large as 1 cm in materials of significance for major engineering structures. Generally, toughness increases and transition temperature decreases as crack size decreases, but these beneficial effects can be nullified by stress triaxiality. Detailed calculations are performed for a buried crack and an edge crack under conditions of plane strain and for a penny-shaped crack loaded axisymmetrically. The plane strain calculations are supplemented by ‘boundary layer’ calculations, in which the effect of specimen geometry appears through a single parameter. The close agreement of the ‘boundary layer’ calculations with the full specimen calculations offers the prospect of a simple characterization of specimen geometry and loading, without the need for geometry-specific computations. The calculations that are reported are, of course, based upon a particular model, chosen in part for com­putational convenience. Thus, their status is that they display possible trends which may be considered to merit further investigation, both theoretical and experimental.

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