Discontinuity waves of orderr?1 in an inhomogeneous anisotropic linear elastic solid

1989 ◽  
Vol 80 (3-4) ◽  
pp. 179-190
Author(s):  
M. C. Patria
Keyword(s):  
Elastic Solid ◽  
Linear Elastic ◽  
Discontinuity Waves

Crack-Path Effect on Material Toughness

1990 ◽  
Vol 57 (1) ◽  
pp. 97-103 ◽  
Author(s):  
Asher A. Rubinstein
Keyword(s):  
Crack Path ◽  
Numerical Procedure ◽  
Crack Tip ◽  
Elastic Solid ◽  
Singular Integral Equations ◽  
Length Change ◽  
Curvilinear Crack ◽  
Linear Elastic ◽  
System Of Cracks ◽  
Remote Stress

The material-toughening mechanism based on the crack-path deflection is studied. This investigation is based on a model which consists of a macrocrack (semi-infinite crack), with a curvilinear segment at the crack tip, situated in a brittle solid. The effect of material toughening is evaluated by comparison of the remote stress field parameters, such as the stress intensity factors (controlled by a loading on a macroscale), to effective values of these parameters acting in the vicinity of a crack tip (microscale). The effects of the curvilinear crack path are separated into three groups: crack-tip direction, crack-tip geometry pattern-shielding, and crack-path length change. These effects are analyzed by investigation of selected curvilinear crack patterns such as a macrocrack with simple crack-tip kink in the form of a circular arc and a macrocrack with a segment at the crack tip in the form of a sinusoidal wave. In conjunction with this investigation, a numerical procedure has been developed for the analysis of curvilinear cracks (or a system of cracks) in a two-dimensional linear elastic solid. The formulation is based on the solution of a system of singular integral equations. This numerical scheme was applied to the cases of finite and semi-infinite cracks.

scholarly journals The influence of elastic deformations in high-strength structural materials on the hydrogen transport

2021 ◽  
Vol 225 ◽  
pp. 01010
Author(s):  
Polina Grigoreva ◽  
Elena Vilchevskaya ◽  
Vladimir Polyanskiy
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Elastic Solid ◽  
High Strength ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Coupled Diffusion ◽  
Elastic Boundary ◽  
Linear Effects ◽  
Solid System

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

Study on the Relationship Between Interaction Factors and Stress Intensity Factor for Elliptical Flaws

2017 ◽  
Author(s):  
Kisaburo Azuma ◽  
Yinsheng Li ◽  
Kunio Hasegawa
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Elastic Solid ◽  
Element Analysis ◽  
Linear Elastic ◽  
Close Proximity ◽  
Interaction Factors ◽  
The Relationship

The interaction of multiple flaws in close proximity to one another may increase the stress intensity factor of the flaw in structures and components. This interaction effect is not distributed uniformly along the crack front. For instance, the strongest interaction is generally observed at the point closest to a neighboring flaw. For this reason, the closest point could show a higher value of the stress intensity factor than all other points in some cases, even if the original value at the point of the single flaw is relatively low. To clarify the condition when the closest point shows the maximum stress intensity factor, we investigated the interaction of two similar elliptical flaws in an infinite model subjected to remote tension loading. The stress intensity factor of the elliptical flaws was obtained by performing finite element analysis of a linear elastic solid. The results indicated that the interaction factors along the crack front can be expressed by a simple empirical formula. Finally, we show the relationship between geometrical features of the flaw and the stress intensity factor at the closest point to a neighboring flaw.

True bounds on Poisson's ratios for transversely isotropic solids

1992 ◽  
Vol 27 (1) ◽  
pp. 43-44 ◽  
Author(s):  
P S Theocaris ◽  
T P Philippidis
Keyword(s):  
Energy Density ◽  
Basic Principle ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Linear Elastic ◽  
Positive Strain ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

The basic principle of positive strain energy density of an anisotropic linear or non-linear elastic solid imposes bounds on the values of the stiffness and compliance tensor components. Although rational mathematical structuring of valid intervals for these components is possible and relatively simple, there are mathematical procedures less strictly followed by previous authors, which led to an overestimation of the bounds and misinterpretation of experimental results.

Separable K-Canonical Formulation of Rectangular Element and Symplectic Integration Method for Analysis of Laminated Plates

2011 ◽  
Vol 194-196 ◽  
pp. 1496-1505
Author(s):  
Guang Hui Qing ◽  
Liang Wang ◽  
Li Zhong Shi
Keyword(s):  
Three Dimensional ◽  
Elastic Solid ◽  
Canonical System ◽  
Laminated Plates ◽  
Linear Elastic ◽  
Canonical Formulation ◽  
Single Plate ◽  
Static Responses ◽  
Rectangular Element ◽  
Symplectic Schemes

In the state space framework, a separable K-canonical formulation of rectangular element and explicit symplectic schemes for the static responses analysis of three-dimensional (3D) laminated plates are proposed in this paper. Firstly, the modified Hellinger-Reissner (H-R) variational principle for linear elastic solid is simply mentioned. Secondly, the separable J-canonical system with Hamiltonian H and the separable K-canonical formulation of rectangular element are constructed. Thirdly, on the basis of the symplectic difference schemes, the explicit symplectic schemes are employed to solve the separable K-canonical governing equation for a single plate. Then, to obtain the high accurate numerical results, a multi-scale iterative technique is also presented. Finally, based on the interlaminar compatibility condition (displacements and stresses), the excellent performance of the method presented in this paper is demonstrated by several numerical experiments of the static responses of laminated plates.

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

scholarly journals Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids

1975 ◽  
Vol 19 (1) ◽  
pp. 40-54 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Existence Of Solutions ◽  
Lateral Displacement ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Elastic Solids ◽  
Standard Potential ◽  
Linear Elastic ◽  
Axis Of Symmetry ◽  
Uniqueness And Existence ◽  
Traction Boundary Conditions

AbstractA plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.

Non-linear analysis of shallow cracks in smooth and notched plates Part 1: Analytical evaluation

2005 ◽  
Vol 40 (3) ◽  
pp. 237-244 ◽  
Author(s):  
G Härkegärd ◽  
A Wormsen
Keyword(s):  
Large Scale ◽  
Elastic Solid ◽  
Linear Analysis ◽  
Single Edge ◽  
Linear Elastic ◽  
Cracked Plate ◽  
Perfectly Plastic ◽  
Double Edge ◽  
Non Linear ◽  
Scale Yielding

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The proposed equation for estimating J makes use of the linear elastic and the fully plastic solution to interpolate over the entire range from small- to large-scale yielding. The elastic geometry factor is obtained by means of the stress intensity factor. In the fully plastic formulation, the plastic geometry factors are obtained by considering a pure power-hardening solid, which reduces at one limit to an incompressible linear elastic solid, and at the other to a perfectly plastic solid. The solutions are given for three basic configurations: a double-edge-cracked plate under tension and bending; a notched plate under tension with a crack at the root of the notch; a single-edge-cracked plate under bending. Both force control and displacement control are considered. The accuracy of the formulae is assessed using the finite element calculations in Part 2.

Modeling Passive Mechanical Interaction Between Aqueous Humor and Iris

2001 ◽  
Vol 123 (6) ◽  
pp. 540-547 ◽  
Author(s):  
Jeffrey J. Heys ◽  
Victor H. Barocas ◽  
Michael J. Taravella
Keyword(s):  
Aqueous Humor ◽  
Elastic Solid ◽  
Ultrasound Biomicroscopy ◽  
Mechanical Interaction ◽  
The Finite Element Method ◽  
Mesh Motion ◽  
Linear Elastic ◽  
Aqueous Humor Flow ◽  
Clinical Observations ◽  
Coupled Equation

Certain forms of glaucoma are associated with displacement of the iris from its normal contour. We present here a mathematical model of the coupled aqueous humor–iris system that accounts for the contribution of aqueous humor flow and passive iris deformability to the iris contour. The aqueous humor is modeled as a Newtonian fluid, and the iris is modeled as a linear elastic solid. The resulting coupled equation set is solved by the finite element method with mesh motion in response to iris displacement accomplished by tracking a pseudo-solid overlying the aqueous humor. The model is used to predict the iris contour in healthy and diseased eyes. The results compare favorably with clinical observations, supporting the hypothesis that passive iris deformation can produce the iris contours observed using ultrasound biomicroscopy.

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