Dynamic Crack Analysis Under Coupled Thermoelastic Assumption

In the present study, an alternative strategy for elasto-dynamic crack problems using boundary element method is discussed. The Laplace transformation is applied to time variation in the formulation. Since the numerical solutions are obtained in the Laplace-transformed domain, the numerical-inverse Laplace transformation is adopted to obtain time histories of the solutions. In the present method, the distributions of the displacement and traction in the vicinity of the crack tip are expressed as the superposition of singular terms and regular ones. The singular terms are the analytical solutions including stress intensity factors of Modes I and II, while the regular terms are approximated by the discrete polynomial functions in general BEM formulations. Additionally, the ligament side is discretized by singular-type crack elements in order to increase the accuracy of the traction near the crack tip. It is shown that the dynamic stress intensity factors (DSIFs) of Modes I and II are determined directly without supplementary procedures such as extrapolation or J-integral scheme. The validity of the present method is confirmed through the analysis of mixed mode dynamic problems of crack.

A subregion DRBEM formulation for the dynamic analysis of two-dimensional cracks

Time-domain BEM for dynamic crack analysis

Due to a very short time span of dynamic fracture event, it is quite difficult to experimentally measure dynamic stress field near the crack tip. Node-based finite element method (NBFEM) developed by Yagawa et al was extended to solve dynamic crack propagation problems by modifying the original NBFEM and three schemes of crack tip node separation during crack propagation are examined. A dynamic stress intensity factor in mode I, KdynI, is calculated for fast propagating crack at a constant speed. Three different schemes of the crack tip node separation were considered. Comparing the numerical results with those analytically obtained by Freund showed that the condition of zero initial velocity and nonzero acceleration gives the highest accuracy of three conditions with only 0.91% error.

The use of quarter point element in dynamic crack analysis

Numerical study on bi-material interface crack using symplectic analytical singular element

Transient elastodynamic crack analysis by time-domain boundary element method (BEM) is presented. Time-dependent traction boundary integral equations (BIEs) are used for this purpose. Both the hypersingular and the non-hypersingular formulations are dealt with. The time-domain traction BIEs are solved numerically by a time-stepping scheme. The efficiency and the accuracy of the time-domain BEM for transient elastodynamic crack analysis are demonstrated by a numerical example. Advantages and drawbacks of the hypersingular and the non-hypersingular BEM formulations are compared and discussed.

In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.

Dynamic analysis of cracks using the SGBEM for elastodynamics in the Laplace-space frequency domain

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Several simple formulas have been developed to predict the variations of stress intensity factors for mode I crack induced by the stiffness and geometry of the near crack-tip inclusion. The derivation of the fundamental formula is based on the transformation toughening theory. The unconstrained mismatch strains between matrix and inclusion, which induce the variation of the near crack-tip field, are estimated based on the Eshelby equivalent inclusion approach. As validated by numerical examples, the developed formulas have satisfactory accuracy for a wide range of the modulus ratio between inclusion and matrix as long as the inclusion is located in the K 0-controlled field.

Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface

A two-level nesting smoothed extended meshfree method for static and dynamic fracture mechanics analysis of orthotropic materials

Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM

Mixed-mode dynamic stress intensity factors by variation technique with finite block method