Accurate Description of Near-Crack-Tip Fields for the Estimation of Inelastic Zone Extent in Quasi-Brittle Materials

2012 ◽  
Vol 525-526 ◽  
pp. 529-532 ◽  
Author(s):  
Václav Veselý ◽  
Jakub Sobek ◽  
Lucie Šestáková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element ◽  
Order Term ◽  
Higher Order ◽  
Fe Analysis ◽  
Displacement Fields ◽  
Deterministic Method ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
Higher Order Term ◽  
Selection Of

A description of stress and displacement fields by means of the Williams power series using also higher-order terms is the focus of this paper. Coefficients of this series are determined via the over-deterministic method from the results of conventional finite element (FE) analysis. A study is conducted into the selection of the FE node set whose results are processed in this regression technique. Coefficients up to the twelfth term were determined with high precision. The effect of the position of the FE node set on the accuracy of the values of the higher-order term coefficients is reported.

Convergence Study on Application of the Over-Deterministic Method for Determination of Near-Tip Fields in a Cracked Plate Loaded in Mixed-Mode

2012 ◽  
Vol 249-250 ◽  
pp. 76-81 ◽  
Author(s):  
Lucie Šestáková ◽  
Václav Veselý
Keyword(s):  
Mixed Mode ◽  
Brittle Materials ◽  
Higher Order ◽  
Displacement Fields ◽  
Deterministic Method ◽  
Crack Behavior ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
Convergence Study

Multi-parameter description of crack behavior in quasi-brittle materials offers still enough space for investigations. Several studies have been carried out by the authors in this field [1-3]. One part of the publications by the authors (this work included) contain analyses of the accuracy, convergence and/or tuning of the over-deterministic method that enables determination of the coefficients of the higher-order terms in Williams expansion approximating the stress and displacement fields in a cracked body without any complicated FE formulations. These intermediate studies should bring together a list of recommendations how to use the ODM as effectively as possible and obtain reliable enough values of coefficients of the higher-order terms. Thus, the stress/displacement field can be determined precisely even in a larger distance from the crack tip, which is crucial for assessment of the fracture occurring in quasi-brittle materials.

Evaluation of Crack Tip Stress Field Using Combination of Advanced Implementation of Over-Deterministic Method and FE Analysis

2014 ◽  
Vol 627 ◽  
pp. 273-276 ◽  
Author(s):  
Jakub Sobek ◽  
T. Pail ◽  
Václav Veselý
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stress Field ◽  
Crack Tip ◽  
Fe Analysis ◽  
Deterministic Method ◽  
Element Analysis ◽  
Java Programming ◽  
Higher Order Terms ◽  
Selection Of

Creation of an automatic utility to determine the values of coefficients of higher order terms of Williams power series by usage of over-deterministic method applied to results of finite element analysis is a main goal of this research. The developed procedure based on the support of Java programming language considerably simplifies analyses on optimization of selection of FE nodal results for improvement of accuracy of the near-crack-tip fields’ approximation using Williams series.

Stress Behavior at the Interface Junction of an Elastic Inclusion

2002 ◽  
Vol 69 (6) ◽  
pp. 844-852 ◽  
Author(s):  
Z. Q. Qian ◽  
A. R. Akisanya ◽  
D. S. Thompson
Keyword(s):  
Finite Element ◽  
Elastic Inclusion ◽  
Symmetric Mode ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Two Phase ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
The Matrix ◽  
Finite Element Prediction

The stress distribution at the interface junction of an elastic inclusion embedded in a brittle matrix is examined. Solutions are derived for the stress and displacement fields near the junction formed by the intersection of the interfaces between the inclusion and the matrix. The stress field consists of symmetric (mode I) and skew-symmetric (mode II) components. The magnitude of the intensity factor associated with each mode of deformation is determined using a combination of the finite element method and a contour integral. The numerical results of the stresses near the interface junction of two different inclusion geometries show that the asymptotic solutions of the stresses are in agreement with those from the finite element prediction when higher-order terms are considered. The implications of the results for the failure of particle-reinforced and two-phase brittle materials are discussed.

Derivation of Skyrme Lagrangian and higher-order term

1990 ◽  
Vol 41 (9) ◽  
pp. 2930-2932
Author(s):  
Akihiro Ito
Keyword(s):  
Order Term ◽  
Higher Order ◽  
Higher Order Term

Higher‐order moveout spectra

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1193-1207 ◽  
Author(s):  
Bruce T. May ◽  
Donald K. Straley
Keyword(s):  
Fourth Order ◽  
Seismic Reflection ◽  
Order Term ◽  
Higher Order ◽  
Second Order ◽  
Equation Modeling ◽  
Fourth Order Term ◽  
Higher Order Terms ◽  
Velocity Spectra

Higher‐order terms in the generalized seismic reflection moveout equation are usually neglected, resulting in the familiar second‐order, or hyperbolic, moveout equation. Modeling studies show that the higher‐order terms are often significant, and their neglect produces sizable traveltime residuals after correction for moveout in such cases as kinked‐ray models. Taner and Koehler (1969) introduced velocity spectra for estimating stacking velocity defined on the basis of second‐order moveout. Through the use of orthogonal polynomials, an iterative procedure is defined that permits computation of fourth‐order moveout spectra while simultaneously upgrading the previously computed, second‐order spectra. Emphasis is placed on the fourth‐order term, but the procedure is general and can be expanded to higher orders. When used with synthetic and field recorded common‐midpoint (CMP) trace data, this technique produces significant improvements in moveout determination affecting three areas: (1) resolution and interpretability of moveout spectra, (2) quality of CMP stacked sections, and (3) computation of velocity and depth for inverse modeling.

Application of the Williams Expansion near a Bi-Material Interface

2017 ◽  
Vol 754 ◽  
pp. 206-209 ◽  
Author(s):  
Lucie Malíková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Tip ◽  
Higher Order ◽  
Simplified Model ◽  
The Finite Element Method ◽  
Material Interface ◽  
Higher Order Terms ◽  
Element Method ◽  
Crack Tip Stress

A simplified model of a crack approaching a bi-material interface is modelled by means of the finite element method in order to investigate the significance of the higher-order terms of the Williams expansion for the proper approximation of the opening crack-tip stress near the bi-material interface. The discussion on results is presented and the importance of the higher-order terms proved.

Differentiation of Mass and Stiffness Matrices for High Order Sensitivity Calculations in Finite Element-Based Equilibrium Problems

1993 ◽  
Vol 115 (4) ◽  
pp. 829-832 ◽  
Author(s):  
J. E. Bernard ◽  
S. K. Kwon ◽  
J. A. Wilson
Keyword(s):  
Finite Element ◽  
Design Variable ◽  
Equilibrium Problems ◽  
Higher Order ◽  
High Order ◽  
Stiffness Matrices ◽  
Higher Order Terms ◽  
Fixed Boundaries ◽  
Cubic Polynomials ◽  
Derivatives Of

Extension of sensitivity methods to include higher order terms depends on the ability to compute higher order derivatives of the mass and stiffness matrices. This paper presents a method based on the use of cubic polynomials to fit mass and stiffness matrices across a range of interest of the design variable. The method is illustrated through an example which uses Pade´ approximants to expand the solution to a statics problem. The design variable is the thickness of one part of a plate with fixed boundaries. The solution gives a very good approximation over fivefold change in the value of the design variable.

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