A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.

Cracking particles: A simplified meshfree method for arbitrary evolving cracks

A three dimensional large deformation meshfree method for arbitrary evolving cracks

A simple and robust three-dimensional cracking-particle method without enrichment

http://user.engineering.uiowa.edu/~sxiao/paper/stable_particleMethods.pdf

Stable particle methods based on Lagrangian kernels

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

SUMMARY The simulation of concrete fragmentation under explosive loading by a meshfree Lagrangian method, the smooth particle hydrodynamics method (SPH) is described. Two improvements regarding the com- pleteness of the SPH-method are examined, �rst a normalization developed by Johnson and Beissel (NSPH) and second a moving least square (MLS) approach as modied by Scheer (MLSPH). The SPH-Code is implemented in FORTRAN 90 and parallelized with MPI. A macroscopic constitutive law with isotropic damage for fracture and fragmentation for concrete is implemented in the SPH-Code. It is shown that the SPH-method is able to simulate the fracture and fragmentation of concrete slabs under contact detonation. The numerical results from the dierent SPH-methods are compared with the data from tests. The good agreement between calculation and experiment suggests that the SPH-program can predict the correct maximum pressure as well as the damage of the concrete slabs. Finally the fragment distributions of the tests and the numerical calculations are compared. Copyright ? 2003 John Wiley & Sons, Ltd.

J. Eibl

Papers

Simulation of high velocity concrete fragmentation using SPH/MLSPH

A numerical model for reinforced concrete structures