Abstract
The phase field fracture method is attracting significant interest. Phase field approaches have enabled predicting - on arbitrary geometries and dimensions - complex fracture phenomena such as crack branching, coalescence, deflection and nucleation. In this work, we present a simple and robust implementation of the phase field fracture method in the commercial finite element package Abaqus. The implementation exploits the analogy between the phase field evolution law and the heat transfer equation, enabling the use of Abaqus’ in-built features and circumventing the need for defining user elements. The framework is general, and is shown to accommodate different solution schemes (staggered and monolithic), as well as various constitutive choices for preventing damage under compression. The robustness and applicability of the numerical framework presented is demonstrated by addressing several 2D and 3D boundary value problems of particular interest. Focus is on the solution of paradigmatic case studies that are known to be particularly demanding from a convergence perspective. The results reveal that our phase field fracture implementation can be readily combined with other advanced computational features, such as contact, and deliver robust and precise solutions. The code developed can be downloaded from www.empaneda.com/codes.
Highlights
Modelling the morphology of an evolving interface is considered to be a longstanding mathematical and computational challenge
The temporal evolution of the phase field variable φ is described by a partial differential equation (PDE) and the method enables the simulation of complex interface evolution phenomena by integrating a set of PDEs for the whole system, avoiding the explicit treatment of interface conditions
We shall consider the case of unstable crack growth in a notched squared plate undergoing uniaxial tension. This is a paradigmatic benchmark in the phase field fracture community since the early work by Miehe et al (2010b)
Summary
Modelling the morphology of an evolving interface is considered to be a longstanding mathematical and computational challenge. The coupling of the phase field paradigm with the variational approach to fracture presented by Bourdin et al (2008) has opened new horizons in the modelling of cracking phenomena, from predicting complex crack trajectories to simulating inertia-driven crack branching This can be achieved on the original finite element mesh, without ad hoc crack propagation criteria, and for arbitrary geometries and dimensions. We circumvent this issue by exploiting the analogy between the heat conduction equation and the phase field evolution law This approach enables using the vast majority of Abaqus’ in-built features, including the coupled temperature-displacement elements from its finite element library, which avoids coding user-defined elements and the associated complications in meshing and visualisation (e.g., Abaqus2Matlab is frequently used to pre-process input files, Papazafeiropoulos et al, 2017).
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