A computational framework for crack propagation in spatially heterogeneous materials

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. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Analysis of the bi-material interface cracks based on configurational forces

In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack tip configurational forces as driving force is introduced to describe the interface crack evolution under mixed mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant of configurational forces with interface fracture toughness. The analytical expression of the configurational forces are obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack tip configurational forces with classical complex intensity factors are obtained through strict mathematical deduction. The interface crack tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bi-material oscillation index. The configurational forces based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for analysis of interface fracture under complex loading conditions.