Adaptive modelling of dynamic brittle fracture - a combined phase field regularized cohesive zone model and scaled boundary finite element approach

Natarajan, Sundararajan; Ooi, Ean Tat; Birk, Carolin; Song, Chongmin

doi:10.1007/s10704-022-00634-2

Cited by 28 publications

(2 citation statements)

References 45 publications

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“…The field variables are constructed from Equation (39) with

\mathbf{u}\left(\xi, \eta \right)=\left[u\left(\xi, \eta \right)\kern1em v\Big(\xi, \eta \Big)\right]\equiv \mathbf{p}\left(\xi, \eta \right)

representing the displacement field and

\phi \left(\xi, \eta \right)\equiv \mathbf{p}\left(\xi, \eta \right)

representing the phase field variable. The discretization of the coupled governing equations follows similarly from that presented in Reference 71 where the general form of shape functions replace the scaled boundary shape functions for the displacement field.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation

Xiao

Natarajan

Birk

et al. 2023

Numerical Meth Engineering

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SummaryA general technique to develop arbitrary‐sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well‐known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well‐established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near‐incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed.

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“…The field variables are constructed from Equation (39) with

\mathbf{u}\left(\xi, \eta \right)=\left[u\left(\xi, \eta \right)\kern1em v\Big(\xi, \eta \Big)\right]\equiv \mathbf{p}\left(\xi, \eta \right)

representing the displacement field and

\phi \left(\xi, \eta \right)\equiv \mathbf{p}\left(\xi, \eta \right)

Section: Numerical Examplesmentioning

confidence: 99%

“…A staggered solution scheme is adopted to solve the coupled equations. The phase field variable is assumed to be constant over a cell and is averaged from the phase field values at the nodes, similar to the approach adopted in Reference 71.…”

Section: Numerical Examplesmentioning

confidence: 99%

Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation

Xiao

Natarajan

Birk

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

On the use of scaled boundary shape functions in adaptive phase field modeling of brittle fracture

Birk,

Pasupuleti,

Assaf

et al. 2024

Comput Mech

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This paper addresses the numerical modeling of brittle fracture using a phase field approach. We propose solving the coupled phase field / displacement problem by employing the scaled boundary finite element method, which facilitates the use of hierarchical meshes. An adaptive meshing approach based on this method is summarized. Contrary to existing applications of the scaled boundary finite element method in the context of phase field modeling, scaled boundary shape functions are employed in both staggered and monolithic solution schemes. The proposed methodology is verified considering two-dimensional benchmark problems. Very good agreement with finite element results of the force-displacement curves and crack paths is observed regardless of the solution scheme or meshing strategy.

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An adaptive mesh refinement algorithm for phase-field fracture models: Application to brittle, cohesive, and dynamic fracture

Gupta

Krishnan

Mandal

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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Adaptive modelling of dynamic brittle fracture - a combined phase field regularized cohesive zone model and scaled boundary finite element approach

Cited by 28 publications

References 45 publications

Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation

Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation

On the use of scaled boundary shape functions in adaptive phase field modeling of brittle fracture

An adaptive mesh refinement algorithm for phase-field fracture models: Application to brittle, cohesive, and dynamic fracture

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