N.Hataf - Associate professor
M.Hajiazizi - ph.D student
A.Ghahramani - professor

Cracks propagations, fragmentations and large deformation of engineering solid materials are characterized by a continuous change in the geometry of the domain under consideration . Conventional methods such ad finite element and finite difference methods use meshes to model and analyze the material behavior .The analysis of large deformation and crack propagation of engineering problems by these methods may require the continuous remeshing of the domain in order to avoid the break down of the calculation due to excessive mesh distortion. In the analysis when even only a few meshes are needed , mesh generation can consume more time and effort compared to the construction and solution of the discrete set of equations. In this paper the essential boundary condition with the enforcing of penalty methods is modified. A more recently introduced mesh-free method which provides an attractive solution to this kind of problems is presented. In this method, the domain is represented by a set of arbitrary distributed nodes and there is no need to use meshes or element for field variable interpolation . The nodes remain constant while the geometry of the domain is changing, therefore saving time and computational effort in analyzing process. A few examples of application of the method in predicting the behavior of materials with large deformations are presented and its suitability is highlighted/

Numerical Method , Meshless Methods , Element Free Galerkin Method