Numerical simulation of adiabatic and isothermal cracks in functionally graded materials using optimized element-free Galerkin method

2017 ◽  
Vol 40 (7) ◽  
pp. 846-865 ◽  
Author(s):  
Sahil Garg ◽  
Mohit Pant
Keyword(s):  
Numerical Simulation ◽  
Galerkin Method ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Element Free Galerkin Method ◽  
Graded Materials ◽  
Element Free Galerkin ◽  
Element Free

A New Interaction Integral Method for Mesh-Free Analysis of Cracks in Functionally Graded Materials

2002 ◽  
Author(s):  
B. N. Rao ◽  
S. Rahman
Keyword(s):  
Functionally Graded Materials ◽  
Meshless Method ◽  
Mixed Mode ◽  
Functionally Graded ◽  
Mixed Mode Fracture ◽  
Smooth Functions ◽  
Graded Materials ◽  
Element Free Galerkin ◽  
Mesh Free ◽  
Element Free

This paper presents a Galerkin-based meshless method for calculating stress-intensity factors (SIFs) for a stationary crack in two-dimensional functionally graded materials of arbitrary geometry. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial co-ordinates and two newly developed interaction integrals for mixed-mode fracture analysis. These integrals can also be implemented in conjunction with other numerical methods, such as the finite element method (FEM). Five numerical examples including both mode-I and mixed-mode problems are presented to evaluate the accuracy of SIFs calculated by the proposed EFGM. Comparisons have been made between the SIFs predicted by EFGM and available reference solutions in the literature, generated either analytically or by FEM using various other fracture integrals or analyses. A good agreement is obtained between the results of the proposed meshless method and the reference solutions.

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