A smoothed particle hydrodynamics approach for phase field modeling of brittle fracture
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by
Mohammad Naqib Rahimi, Georgios Moutsanidis
2022
Abstract
Fracture is a very challenging and complicated problem with various
applications in engineering and physics. Although it has been extensively
studied within the context of mesh-based numerical techniques, such as the
finite element method (FEM), the research activity within the Smoothed Particle
Hydrodynamics (SPH) community remains scarce. SPH is a particle based method,
ideal to simulate fracture scenarios that involve extreme deformations.
However, to model fracture, SPH researchers have mostly relied on ad-hoc
empirical local damage models, cohesive zone approaches, or pseudo-spring
models, which come with a set of drawbacks and limitations. On the other hand,
phase field models of brittle fracture have recently gained popularity in
academic circles and provide significant improvements compared to previous
approaches. These improvements include the derivation from fundamental fracture
theories, the introduction of non-locality, and the ability to model multiple
crack initiation, propagation, branching, and coalescence, in situations where
no prior knowledge of the crack paths is available. Nevertheless, phase field
modeling has not been combined with SPH for fracture simulations. In this
proof-of-concept paper we develop and implement a phase field model of brittle
fracture within the context of SPH. Comprehensive mathematical and
implementation details are provided, and several challenging numerical examples
are computed and illustrate the proposed method's ability to accurately and
efficiently simulate complex fracture scenarios with the SPH framework.
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