Keywords: EFGM, cohesive crack, crack growth, concrete.

In the paper the idea of extended finite element method is applied to the element free Galerkin method (EFGM) [2]. The enrichment approximation of the displacement field can be written in the form

where is the matrix of standard shape functions derived using weighted moving least square method, is the vector of standard displacement degrees of freedom, is the matrix of additional degrees of freedom associated with the enrichment functions and is the Boolean matrix. The enrichment functions are selected from the solution of the linear elastic fracture mechanics.

In EFGM algorithm, the computations of the shape functions and their derivatives are made using the consistency condition [1]. In calculations of the crack propagation, the Hilleborg's fictitious crack model is extended on the case in which the crack growth is a combinations of opening mode I and sliding mode II [3].

Finally, the incremental set of equations is built and solved iterativly, using the Newton-Raphson method.

The method described above has been applied to the 2D analysis of plain concrete structures. Results of computations are in good agreement with the known solutions, however, using the enrichment approximations of the displacement field considerably has improved efficiency of the analysis.

1

A. Huerata ans S.F. Mendez. Enrichment and coupling of the finite element and meshless methods. International Journal for Numerical Methods in Engineering, 48:1615-1636, 2000. doi:10.1002/1097-0207(20000820)48:11<1615::AID-NME883>3.0.CO;2-S

2

Cz. Cichon and J. Jaskowiec. Coupling generalized fc model to meshless efg method for crack growth analysis in quasi-brittle materials. CAMES, 8:543-556, 2001.

3

G.N. Wells. Discontinuous modelling of strain localisation and failure. Dissertation, Delft University of Technology, The Netherlands, 2001.

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