A coupled finite element (FE) and element free Galerkin (EFG) approach is used to simulate 3-D stochastic quasi-static fatigue crack growth problems. In this approach, a region near the crack is modelled by EFG, and rest is modelled by FE. A ramp function is utilised to model the transition between FE and EFG domains. Crack growth is modelled by joining the crack increments at the ends through cubic spline segments to obtain a modified crack front. The effect of load and Paris constant is studied on the fatigue life. The probability of failure is obtained using Weibull probability distribution function. © 2015 Elsevier Ltd.

Pathak H.

Singh A.

Singh I.V.

Brahmankar M.

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Shiv Nadar University

Computers and Structures

In this work, finite element method (FEM) and element free Galerkin method (EFGM) are coupled for solving 3D crack domains subjected to cyclic thermal load of constant amplitude. Crack growth contours and fatigue life have been obtained for each of the considered numerical examples. Thermo-elastic problems are decoupled into thermal and elastic problems. Firstly, the unknown temperature field is obtained by solving heat conduction equation, then, it is used as the input load in the elastic problem to calculate the displacement and stress fields. The geometrical discontinuity across crack surface is modelled by extrinsically enriched EFGM and the remaining part of the domain is approximated by standard finite element method. At the crack interface, a ramp function based interpolation scheme has been implemented. This coupled approach combines the advantages of both EFGM and FEM. A linear successive crack increment approach is used to model crack growth. The growing crack surface is traced by level set function. Standard Paris law is used for life estimation of the three-dimensional crack models. Different cases of planar and non-planar crack problems have been solved and their results are compared with the results obtained using extended finite element method to check accuracy, efficiency and robustness of the coupled FE-EFG approach implemented in this study. © 2016, The Institution of Engineers (India).

Journal of The Institution of Engineers (India): Series C

Numerical Simulation of 3D Thermo-Elastic Fatigue Crack Growth Problems Using Coupled FE-EFG Approach

This paper presents the three-dimensional interfacial crack growth simulations using coupled finite element and element free Galerkin (FE-EFG) approach under mechanical and thermo-elastic loading. Extrinsic partition of unity (PU) enrichment technique has been employed to model a crack in the domain. Crack face and crack front have been modelled by Heaviside and asymptotic branch enrichment functions respectively whereas a material interface has been modelled by a signed distance function. Modified domain based interaction integral approach has been employed to evaluate the individual stress intensity factors. Standard Paris law of fatigue crack growth has been employed for the life prediction of interfacial cracked geometries. Several interfacial fatigue crack growth problems have been solved by the coupled EF-EFG approach. © 2016 Elsevier Ltd

Theoretical and Applied Fracture Mechanics

Three-dimensional quasi-static interfacial crack growth simulations in thermo-mechanical environment by coupled FE-EFG approach

Applied Mathematical Modelling

Fatigue crack growth simulations of homogeneous and bi-material interfacial cracks using element free Galerkin method

A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields

International Journal of Mechanical Sciences

Fatigue crack growth simulations of 3-D problems using XFEM

A novel enrichment criterion for modeling kinked cracks using element free Galerkin method

Crack growth modeling via 3D automatic adaptive mesh refinement based on modified-SPR technique

Three-dimensional stochastic quasi-static fatigue crack growth simulations using coupled FE-EFG approach