A new Kirchhoff plate model based on a modified couple stress theory

SUMMARY In 3D fracture modeling, the complexity of the evolving crack geometry during propagation raises challenges in stress analysis because the accuracy of results mainly relies on the accurate description of the crack geometry. In this paper, a numerical framework is developed for 3D fracture modeling where a meshless method, the element-free Galerkin method, is used for stress analysis and level sets are used accurately to describe and capture crack evolution. In this framework, a simple and general formulation for associating the displacement jump in the field approximation with an arbitrary 3D curved crack surface is proposed. For accurate closure of the crack front, a tying procedure is extended to 3D from its original use in 2D in the previous paper by the authors. The benefits of level sets in improving the results accuracy and reducing the computational cost are explored, particularly in the model refinement and the confinement of the displacement jump. Issues arising in level sets updating are discussed and solutions proposed accordingly. The developed framework is validated with a number of 3D crack examples with reference solutions and shows strong potential for general 3D fracture modeling. Copyright © 2012 John Wiley & Sons, Ltd.

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling

A numerical method is presented for obtaining the values of K*
1,K
*
II and K*
III in the elasticity solution at the tip of an interface crack in general states of stress. The basis of the method is an evaluation of theJ-integral by the virtual crack extension method. Individual stress intensities can then be obtained from further calculations ofJ perturbed by small increments of the stress intensity factors. The calculations are carried out by the finite element method but minimal extra computations are required compared to those for the boundary value problem. Very accurate results are presented for a crack in the bimaterial interface and compared with other methods of evaluating the stress intensity factors. In particular, a comparison is made with stress intensity factors obtained by computingJ by the virtual crack extension method but separating the modes by using the ratio of displacements on the crack surface. Both techniques work well with fine finite element meshes but the results suggest that the method that relies entirely on J-integral evaluations can be used to give reliable results for coarse meshes.

A method for calculating stress intensities in bimaterial fracture

An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions

Crack tip energy release rate for a piezoelectric compact tension specimen

A path independent contour integral formula for the distinct calculation of combined mode stress intensity factors in linear plane elasticity problems is presented. The method is based on a Somigliana type singular integral representation and is easily appended to existing finite element computer codes. Numerical results to three problems with known perturbation solutions are given and demonstrate the accuracy and stability of the method.

A contour integral computation of mixed-mode stress intensity factors

A general boundary integral formulation for the numerical solution of plate bending problems

Families of two-and three-dimensional finite elements are constructed for use in modelling fields with singular derivatives. The elements are complete over linear fields, conform with regular elements, and are easily programmed. A low order exact quadrature rule is also derived for element stiffness calculations.

Families of consistent conforming elements with singular derivative fields

A reciprocal work contour integral method for calculating stress intensity factors is extended to treat the problem of two bonded dissimilar materials containing a crack along the bond. The method is based on Betti's Reciprocal work theorem from which the singular stress intensities at the crack tip may be evaluated in terms of an integral involving tractions and displacements on a contour remote from the crack tip.

The computation of stress intensity factors in dissimilar materials

The reflection of plane acoustic waves at the water–sediment interface is analyzed. The sediments are modeled using Biot’s equations with depth‐dependent coefficients. Computations are made of the reflection coefficient as a function of the incident wave frequency and angle for representative sediment properties. The results are compared to those obtained by modeling the sediments as a homogeneous viscoelastic material and as a viscoelastic material with depth‐dependent properties. It is shown that both of these models yield predictions of the reflection coefficient that can differ substantially from the Biot model.

Morris Stern

Papers

A contour integral computation of mixed-mode stress intensity factors

A general boundary integral formulation for the numerical solution of plate bending problems

Families of consistent conforming elements with singular derivative fields

The computation of stress intensity factors in dissimilar materials

Wave reflection from a sediment layer with depth-dependent properties