Computational Analysis of Linear Elastic Crack Growth in Functionally Graded Bodies Using Non-Uniform Steps Integrated in the MLPG

Abstract

This paper describes the estimation of mixed-mode crack growth path in functionally graded materials under mechanical and thermal loads by the meshless method. Simple and complex geometries with single and double cracks are provided to verify the merits of a recently proposed modified meshless local Petrov–Galerkin method and to show the applicability of this method in crack growth simulation. Polygon test function domains are constructed locally at every crack growth step in order to numerically calculate contour and domain integrals. The classical form of thin plate spline radial basis function without enrichment with a regular distribution of points in the vicinity of crack tips are used. In this efficient method, the total number of domain points are kept fixed during crack growth steps forever. For this end, a simple method of new crack tip determination at every growth step is proposed. The MLPG results are compared with reference solutions including experimental, finite element, boundary element and other meshless methods and the accuracy of this method is investigated in different numerical test problems.