We analyze the scaling of avalanche precursors in the three dimensional random fuse model by numerical simulations. We find that both the integrated and nonintegrated avalanche size distributions are in good agreement with the results of the global load sharing fiber bundle model, which represents the mean-field limit of the model.

The present manuscript focuses on the algorithmic treatment of three-dimensional discontinuities within a purely displacement based finite element setting. In contrast to two-dimensional cracks, the local element based geometric representation of threedimensional crack surfaces is non-unique and thus not straightforward. Accordingly, we compare different crack tracking strategies, one being alg...

This paper presents a meshless point collocation method for three-dimensional crack propagation. The meshless point collocation method is based on direct discretization of strong-form governing equations to achieve a truly meshless scheme that does not require mesh structures or a numerical integration procedure. These characteristics of the point collocation method enable the direction of an a...

The influence coefficient method, which has advantages for conducting inverse analysis and sensitivity studies, is extended to simulate cohesive cracking in three-dimensional bodies when the crack path is known in advance. The method is combined with a focal point model to allow simulation of unload–reload cycles as well. This paper summarizes the theory behind the influence coefficient method ...

Using large system sizes with extensive statistical sampling, we analyze the scaling properties of crack roughness and damage profiles in the three-dimensional random fuse model. The analysis of damage profiles indicates that damage accumulates in a diffusive manner up to the peak load, and localization sets in abruptly at the peak load, starting from a uniform damage landscape. The global crac...

A two dimensional model which describes the evolution of a crack in a plate is deduced from a three dimensional linearly elastic Griffith’s type model. The result is achieved by adopting the framework of energetic solutions for rate-independent processes, to model three dimensional fracture evolution, in conjunction with a variational dimension reduction procedure.

A numerical technique for modeling fatigue crack propagation of multiple coplanar cracks is presented. The proposed method couples the extended finite element method (X-FEM) [Int. J. Numer. Meth. Engng. 48 (11) (2000) 1549] to the fast marching method (FMM) [Level Set Methods & Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials ...

This paper presents a study of generalized enrichment functions for three-dimensional curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of cur...

A series of massively parallel molecular dynamics simulations with up to 35 million atoms is performed to investigate dislocation emission from a three-dimensional crack. We observe dislocation loops emitted from the crack front|the rst time this has been seen in computer simulations. The sequence of dislocation emission in the process of crack blunting process strongly depends on the crystallo...

The difference in the potential energy in an elastic three-dimensional domain with a V-notch with and without a small crack ( δΠ ) under a general mixed mode I+II+III loading is provided as an asymptotic series. It involves the V-notch edge stress intensity functions, the area of the formed crack, and special geometrical functions that can be pre-computed and tabulated. Importantly, the stress ...