Efficient Implementation of Extended Finite Element Method

2012 ◽  
Author(s):  
Vishal Hotwani ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Extended Finite Element Method ◽  
Exact Analytical Solution ◽  
Crack Tip ◽  
Finite Element Solution ◽  
Element Solution ◽  
Extended Finite Element ◽  
Element Method

Extended finite element method (or XFEM) locally enriches the finite element solution using a priori known analytical solution. XFEM has been used extensively in fracture mechanics to compute stress concentration at crack tips. It is a mesh independent method that allows crack to be represented as an equation instead of using the mesh to approximate it. When this approach is used along with Implicit Boundary Finite Element Method (IBFEM) to apply boundary conditions, a fully mesh independent approach for studying crack tip stresses can be implemented. An efficient scheme for blending the enriched solution structure with the underlying finite element solution is presented. A ramped step function is introduced for modeling discontinuity or a crack within an element. Exact analytical solution is used as enrichment at the crack tip element to obtain the stress intensity factor (SIF) directly without any post processing or contour integral computation. Several examples are used to study the convergence and accuracy of the solution.

scholarly journals The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Xia Xiaozhou ◽  
Zhang Qing ◽  
Wang Hong ◽  
Jiang Qun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Basis Function ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Function Form ◽  
Extended Finite Element ◽  
Polar Radius ◽  
Radius Function ◽  
Element Method

In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.

New anisotropic crack-tip enrichment functions for the extended finite element method

2012 ◽  
Vol 50 (5) ◽  
pp. 591-601 ◽  
Author(s):  
G. Hattori ◽  
R. Rojas-Díaz ◽  
A. Sáez ◽  
N. Sukumar ◽  
F. García-Sánchez
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Crack Tip ◽  
Extended Finite Element ◽  
Element Method

scholarly journals A Cell-Based Smoothed XFEM for Fracture in Piezoelectric Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Li Ming Zhou ◽  
Guang Wei Meng ◽  
Feng Li ◽  
Shuai Gu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Piezoelectric Materials ◽  
Crack Tip ◽  
Extended Finite Element ◽  
Boundary Integration ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Element Method

This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.

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