A computational framework for crack propagation in spatially heterogeneous materials

Pearce, C. , Lewandowski, K. , Kaczmarczyk, Ł. , Athanasiadis, I. and Marshall, J. F. (2021) A computational framework for crack propagation in spatially heterogeneous materials. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 379, 20200291. (doi: 10.1098/rsta.2020.0291)

Abstract

This paper presents a mathematical formulation and numerical modelling framework for brittle crack propagation in heterogeneous elastic solids. Such materials are present in both natural and engineered scenarios. The formulation is developed in the framework of configurational mechanics and solved numerically using the finite-element method. We show the methodology previously established for homogeneous materials without the need for any further assumptions. The proposed model is based on the assumption of maximal dissipation of energy and uses the Griffith criterion; we show that this is sufficient to predict crack propagation in brittle heterogeneous materials, with spatially varying Young’s modulus and fracture energy. Furthermore, we show that the crack path trajectory orientates itself such that it is always subject to Mode-I. The configurational forces and fracture energy release rate are both expressed exclusively in terms of nodal quantities, avoiding the need for post-processing and enabling a fully implicit formulation for modelling the evolving crack front and creation of new crack surfaces. The proposed formulation is verified and validated by comparing numerical results with both analytical solutions and experimental results. Both the predicted crack path and load–displacement response show very good agreement with experiments where the crack path was independent of material heterogeneity for those cases. Finally, the model is successfully used to consider the real and challenging scenario of fracture of an equine bone, with spatially varying material properties obtained from CT scanning.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Athanasiadis, Dr Ignatios and Lewandowski, Dr Karol and Kaczmarczyk, Professor Lukasz and Pearce, Professor Chris and Marshall, Mr John
• Authors: Pearce, C., Lewandowski, K., Kaczmarczyk, Ł., Athanasiadis, I., and Marshall, J. F.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Philosophical Transactions A: Mathematical, Physical and Engineering Sciences
• Publisher: The Royal Society
• ISSN: 1364-503X
• ISSN (Online): 1471-2962
• Copyright Holders: Copyright © 2021 The Royal Society
• First Published: First published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences 379:20200291
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher