Efficient Simulation of Quasi-static and Dynamic Crack Propagation using Enhanced Finite Elements

Abstract

Failure analysis is a crucial step in design and assessment of many concrete structures such as dams, bridges and buildings which entails treatment of cracks and fractures. Given the complexities associated with the mechanics of the problem, this was historically tackled based on crude simplifications. However, the introduction of computers in the mid last century, paved the way towards the use and further development of finite elements methods. In the broad sense, these approaches can be categorised into smeared and discrete crack models. While in the former a crack was represented as a continuum material property, the latter treats the crack more realistically as a discontinuity in the displacement field. In this regard, many state-of-the-art approaches for predicting discrete fracture within the finite element framework were designed by enhancing the continuous displacement field with a discontinuous counterpart. These methods provided unprecedented versatility in simulation of crack propagation with a path independent of the background mesh. However, they come with a range of challenges concerning accuracy and efficiency. Examples are but not limited to inaccurate local stress solutions around the crack, increase in the system dimensions upon crack evolution, and ill-conditioned system of equations. In addition, these methods tend to nullify the critical time step in dynamic cases when an explicit time integration is employed. Aiming at overcoming these issues, this thesis introduces a range of finite element based methods for quasi-static and dynamic crack propagation. The performance of the methods are verified using a wide range of well-known analytical, experimental and numerical data. In terms of efficiency, different criteria such as analysis time in statics and critical time step size in dynamics were considered.