G. P. Nikishkov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.5, pp. 335-361, 2013, DOI:10.3970/cmes.2013.093.335

Abstract Accuracy of the quarter-point and transition elements is investigated on one- and two-dimensional problems with inverse square-root singularity. It is demonstrated that most coefficients of the stiffness matrix of the quarter-point element are unbounded. However, numerical integration produces finite values of these coefficients. Influence of several parameters on the error in determining the stress intensity factor is studied. Solution accuracy can be improved using special distribution of element sizes and increasing the element integration order in the radial direction. More >

Yasunori Yusa¹, Shinobu Yoshimura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.6, pp. 445-461, 2013, DOI:10.3970/cmes.2013.091.445

Abstract For large-scale fracture mechanics simulation, a partitioned iterative coupling method is investigated. In this method, an analysis model is decomposed into two domains, which are analyzed separately. A crack is introduced in one small domain, whereas the other large domain is a simple elastic body. Problems concerning fracture mechanics can be treated only in the small domain. In order to satisfy both geometric compatibility and equilibrium on the domain boundary, the two domains are analyzed repeatedly using an iterative solution technique. A benchmark analysis was performed in order to validate the method and evaluate its computational performance. The computed stress… More >

Mohammad Mashayekhi¹, Hossein M. Shodja^1,2, Reza Namakian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 19-60, 2011, DOI:10.3970/cmes.2011.076.019

Abstract A meshless method called reproducing kernel particle method (RKPM) is exploited to cope with elastic-plastic fracture mechanics (EPFM) problems. The idea of arithmetic progression is assumed to place particles within the refinement zone in the vicinity of the crack tip. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. Also, a tracking to find the appropriate diffraction parameter is performed. To assess the suggestions made, two mode I numerical simulations, pure tension and pure bending tests, are executed. Results including J integral, crack mouth opening displacement (CMOD), and plastic zone size and shape are compared… More >

H.X. Wang, S.X. Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 253-274, 2008, DOI:10.3970/cmes.2008.035.253

Abstract In the meshfree cohesive crack method, the discrete crack is modeled by a set of cohesive crack segments which can be arbitrarily oriented. Propagation of the crack is achieved by activation of crack surfaces at individual nodes, so no representation of the crack surface is needed. The crack is modeled by a local enrichment of the test and trial functions with sign function, so that discontinuities are along the direction of the crack. A set of cracking rules is developed to avoid spurious cracking. More >

L.S. Miers¹, J.C.F. Telles²

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 161-170, 2006, DOI:10.3970/cmes.2006.014.161

Abstract This work aims at extending the concept of the Numerical Green's Function (NGF), well known from boundary element applications to fracture mechanics, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals over the crack boundary and is introduced only for source points whose support touches or contains the crack. The results obtained with the coupling of NGF-LBIE in previous potential discontinuity Laplace's equation problems and the authors' experience in NGF-BEM fracture mechanics were the motivation for this development. More >

E. Schnack¹, W. Weber², Y. Zhu³

CMES-Computer Modeling in Engineering & Sciences, Vol.74, No.1, pp. 1-38, 2011, DOI:10.3970/cmes.2011.074.001

Abstract Three dimensional fracture mechanics was done by several groups in the past. One topic for these three dimensional fracture mechanics is to consider re-entrant corners or wedges for isotropic material. An algorithm was developed in the past to compute the dominant eigenvalues for those problems with high accuracy. Based on Kondratiev's Lemma for elliptic boundary value problems it is started with the asymptotic for the displacement and stress distribution around these three dimensional corners. By considering the mixed boundary value problem, the field quantities in the vicinity of corner points are computed by using a special finite element formulation, which… More >

W. J. Feng¹, X. Han², Y.S. Li³

CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.048.001

Abstract The two-dimensional (2D) fracture problem of nonhomogeneous mag -neto-electro-thermo-elastic materials under dynamically thermal loading is investigated by the meshless local Petrov-Galerkin (MLPG) method. The material parameters are assumed to vary in either the height or width direction of the plates. The Laplace-transform technique is utilized to solve the time-dependent problems. In this MLPG analysis, the moving least squares (MLS) method is adopted to approximate the physical quantities, and the Heaviside step function is taken as a test function. The validity and efficiency of the MLPG method are firstly examined. The crack problem of a nonhomogeneous magneto-electro-thermo-elastic plate is then considered.… More >

J.A. Sanz, M. Solis, J. Dominguez¹

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 215-230, 2007, DOI:10.3970/cmes.2007.017.215

Abstract A general mixed boundary element formulation for three-dimensional piezoelectric fracture mechanics problems is presented in this paper. The numerical procedure is based on the extended displacement and traction integral equations for external and crack boundaries, respectively. Integrals with strongly singular and hypersingular kernels appearing in the formulation are analytically transformed into weakly singular and regular integrals. Quadratic boundary elements and quarter-point boundary elements are implemented in a direct way in a computer code. Electric and stress intensity factors are directly computed from nodal values at quarter-point elements. Crack problems in 3D piezoelectric bounded and unbounded solids are solved. The obtained… More >

A.N. Guz¹, O.V. Menshykov^1,2, V.V. Zozulya³, I.A. Guz²

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.3, pp. 205-214, 2007, DOI:10.3970/cmes.2007.017.205

Abstract The contact interaction of opposite faces of an elliptical crack is studied for the case of a normal time-harmonic shear wave loading. The distribution of stress intensity factors (shear modes II and III) as functions of the wave number and the friction coefficient is investigated. The results are compared with those obtained for an elliptical crack without allowance for the contact interaction. More >

S. Hagihara¹, M. Tsunori², T. Ikeda³, N. Miyazaki³

CMES-Computer Modeling in Engineering & Sciences, Vol.17, No.2, pp. 63-72, 2007, DOI:10.3970/cmes.2007.017.063

Abstract The element-free Galerkin (EFG) method is applied to the calculation of elastic-plastic fracture mechanics parameters such as the J-integral and T*-integral. The fields of displacement, strain and stress for a crack problem are obtained using the elastic-plastic EFG method. Then the elastic-plastic fracture mechanics parameters J-integral and T*-integral are calculated from path and domain integrals. In the finite element analysis, paths for the path integral and domains for the domain integral are selected depending on finite element mesh division. On the other hand, they can be arbitrarily selected in the EFG method, and we can use a simple integral path… More >