Numerical solution of stress intensity factors of multiple cracks in great numbers with eigen crack opening displacement boundary integral equations

Abstract

Based on the eigen crack opening displacement (COD) boundary integral equations (BIEs), a newly developed computational approach is proposed for the analysis of multiple crack problems. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity BIEs in an iterative fashion with a small size of system matrix. The interactions among cracks are dealt with by two parts according to the distances of cracks to the current crack. The strong effects of cracks in adjacent group are treated with the aid of the local Eshelby matrix derived from the traction BIEs in discrete form. While the relatively week effects of cracks in far-field group are treated in the iteration procedures. Numerical examples are provided for the stress intensity factors of multiple cracks, up to several thousands in number, with the proposed approach. By comparing with the analytical solutions in the literature as well as solutions of the dual BIEs, the effectiveness and the efficiencies of the proposed approach are verified.

Keywords:

• Multiple cracks
• stress intensity factor
• eigen COD
• boundary integral equation
• local Eshelby matrix

Additional information

Notes on contributors

H Ma

Dr Hang Ma is a professor in the Department of Mechanics, Shanghai University, China. He is an expert in computational solid mechanics with the advanced numerical techniques based on the boundary integral equations. His current research interest is to develop a new numerical technique with eigen variable boundary integral equations for modelling multi-scaled multi-cracked solids with multiple inhomogeneities to make this large-scale simulation problem solvable on desktop computers. He is now the chief research of two projects of the National Nature Science Foundation of China. As the first author, he has published more than 100 peer-reviewed research papers and two books.

Z Guo

Zhao Guo obtained BE and MS degrees in applied mathematics from Hunan University of Science and Engineering and Shanghai University, China, respectively. Now he is studying for his PhD degree at the Shanghai Institute of Applied Mathematics and Mechanics of Shanghai University, with the major of solid mechanics. His current research interests are computational solid mechanics with the advanced numerical techniques using the boundary integral equations with the fast multi-pole techniques for evaluating multiple cracked material and modelling composites. He has participated in two projects that were supported by the National Nature Science Foundation of China and the Graduate Innovation Foundation of Shanghai University, respectively. He has published 5 research papers.

C Yan

Dr Cheng Yan is an associate professor in the School of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Australia. He is an expert in synthesis and characterisation of various materials. His current research interests include fatigue and fracture mechanics, structural and functional nano-composites, biomaterials and biomechanics, nano-mechanics, and modelling at micro- and nano-scales. He has been awarded two competitive ARC fellowships, 10 ARC projects and granted over $5 million research funds. He has generated more than 200 publications.

M Dhanasekar

Prof Manicka Dhanasekar has keen interest in the behaviour of joints in infrastructure and building components. The interest stems from his PhD (1985) from the University of Newcastle, NSW, Australia, where he closely examined the brick C mortar interfaces. Later as an academic he has extended the interface modelling methods to insulated rail joints, which are safety critical devices in the signalling systems of rail network. Effects of inclusions and interfaces between the inclusions and surrounding matrices is of current modelling interest with applications focussed on thin polymer layer mortar/concrete masonry block interfaces. He is a registered professional engineer in Queensland (RPEQ).