Abstract
This paper presents an enhanced theoretical formulation and associated computational framework for brittle fracture in elastic solids within the context of configurational mechanics, building on the authors’ previous paper, Kaczmarczyk et al. (2014). The local form of the first law of thermodynamics provides an equilibrium condition for the crack front, expressed in terms of the configurational forces. Applying the principle of maximal energy dissipation, it is shown that the direction of the crack propagation is given by the direction of the configurational forces. In combination with a fracture criterion, these are utilised to determine the position of the continuously evolving crack front. This exploitation of the crack front equilibrium condition leads to a completely new, implicit, crack propagation formulation. A monolithic solution strategy is adopted, solving simultaneously for both the material displacements (i.e. crack extension) and the spatial displacements. The resulting crack path is resolved as a discrete displacement discontinuity, where the material displacements of the nodes on the crack front change continuously, without the need for mesh splitting or the use of enrichment techniques. In order to trace the dissipative loading path, an arc-length procedure is adopted that controls the incremental crack area growth. In order to maintain mesh quality, smoothing of the mesh is undertaken as a continuous process, together with face flipping, node merging and edge splitting where necessary. Hierarchical basis functions of arbitrary polynomial order are adopted to increase the order of approximation without the need to change the finite element mesh. Performance of the formulation is demonstrated by means of three representative numerical simulations, demonstrating both accuracy and robustness.
Highlights
The serious consequences of cracks in materials and structures mean that the computational modelling of crack propagation continues to be a critical area of research, and a major challenge
Applying the principle of maximal energy dissipation, it is shown that the direction of the crack propagation is given by the direction of the configurational forces
This paper presents a finite element based computational framework for modelling brittle crack propagation in elastic solids, based on the concept of configurational mechanics
Summary
The serious consequences of cracks in materials and structures mean that the computational modelling of crack propagation continues to be a critical area of research, and a major challenge. To formulate the crack propagation problem within the framework of configurational mechanics, two related kinematic descriptions are defined in the spatial and material settings In the former, the classical conservation law of linear momentum balance is described, where Newtonian forces are work conjugate to changes in the spatial position, at fixed material position (i.e. no crack propagation). The authors’ previous paper [20] described the mathematical formulation for crack propagation and a methodology for resolving the evolving crack path within the context of the finite element method, and represented an advancement of the work of Miehe et al [18,19]. Three numerical examples are presented that demonstrate the ability of the formulation to accurately and robustly predict crack paths without bias from the original mesh
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More From: Computer Methods in Applied Mechanics and Engineering
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