scholarly journals Radiation force of stationary elastic compressional and shear plane waves on a cylinder encased in a linear elastic solid

2021 ◽  
Vol 4 ◽  
pp. 100040 ◽  
Author(s):  
F.G. Mitri
Keyword(s):  
Plane Waves ◽  
Elastic Solid ◽  
Radiation Force ◽  
Shear Plane ◽  
Linear Elastic

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.

Development of Constitutive Equation for Infinite Body of Impact Problem

2007 ◽  
Vol 353-358 ◽  
pp. 611-614
Author(s):  
Seung Yong Yang
Keyword(s):  
Finite Element ◽  
Constitutive Equation ◽  
Plane Waves ◽  
Shear Plane ◽  
Material Behavior ◽  
Infinite Body ◽  
Wave Impact ◽  
Finite Element Software ◽  
Impact Simulations ◽  
Impact Problem

A constitutive equation was developed for an infinite body in plane wave impact problem, and implemented using the finite element software ABAQUS user subroutine. Bilinear material behavior under monotonically increasing loading was considered for the constitutive equation. The finite element governed by this type of material behavior can be used as an infinite body transmitting longitudinal and shear plane waves, so that the number of finite elements can be reduced in impact simulations. To test the developed method, results of a plate impact experiment were examined. The numerical results show the accuracy of the developed constitutive equation.

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