NLMech: Implementation of finite difference/meshfree discretization of nonlocal fracture models

Jha, Prashant K.; Diehl, Patrick

doi:10.21105/joss.03020

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…In that case, the predicted strain is 𝜺 = 1 × 10 −8 using the author's C++ code. 47,60 The python code finished in 1.04 s (24 iterations) using the presented approach, and the numerical approximation of the tangent stiffness matrix took 3.71 s (31 iterations).…”

Section: One-dimensionalmentioning

confidence: 99%

“…As a second validation, the same discretized bar was simulated using Silling's state‐based model 2 and the assembly of the tangent stiffness matrix using the numerical approximation of the derivative as in Reference 48. In that case, the predicted strain is

\boldsymbol{\epsilon} =1\times 1{0}^{-8}

using the author's C++ code 47,60 . The python code finished in 1.04

\mathrm{s}

(24 iterations) using the presented approach, and the numerical approximation of the tangent stiffness matrix took 3.71

\mathrm{s}

(31 iterations).…”

Section: Numerical Examplesmentioning

confidence: 99%

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Quasistatic fracture using nonlinear‐nonlocal elastostatics with explicit tangent stiffness matrix

Diehl

Lipton

2022

Numerical Meth Engineering

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We apply a nonlinear‐nonlocal field theory for numerical calculation of quasistatic fracture. The model is given by a regularized nonlinear pairwise potential in a peridynamic formulation. The potential function is given by an explicit formula with an explicit first and second derivatives. This fact allows us to write the entries of the tangent stiffness matrix explicitly thereby saving computational costs during the assembly of the tangent stiffness matrix. We validate our approach against classical continuum mechanics for the linear elastic material behavior. In addition, we compare our approach to a state‐based peridynamic model that uses standard numerical derivations to assemble the tangent stiffness matrix. The numerical experiments show that for elastic material behavior our approach agrees with both classical continuum mechanics and the state‐based model. The fracture model is applied to produce a fracture simulation for a ASTM E8 like tension test. We conclude with an example of crack growth in a pre‐cracked square plate. For the pre‐cracked plate, we investigated load in force (soft loading) and load in displacement (hard loading). Our approach is novel in that only bond softening is used as opposed to bond breaking. For the fracture simulation we have shown that our approach works with and without initial damage for two common test problems.

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Section: One-dimensionalmentioning

confidence: 99%

\boldsymbol{\epsilon} =1\times 1{0}^{-8}

using the author's C++ code 47,60 . The python code finished in 1.04

\mathrm{s}

(24 iterations) using the presented approach, and the numerical approximation of the tangent stiffness matrix took 3.71

\mathrm{s}

(31 iterations).…”

Section: Numerical Examplesmentioning

confidence: 99%

Quasistatic fracture using nonlinear‐nonlocal elastostatics with explicit tangent stiffness matrix

Diehl

Lipton

2022

Numerical Meth Engineering

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The C++ Standard Library for Parallelism and Concurrency (HPX)

Diehl,

Brandt,

Kaiser

2024

Parallel C++

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A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.

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NLMech: Implementation of finite difference/meshfree discretization of nonlocal fracture models

Cited by 10 publications

References 22 publications

Quasistatic fracture using nonlinear‐nonlocal elastostatics with explicit tangent stiffness matrix

Quasistatic fracture using nonlinear‐nonlocal elastostatics with explicit tangent stiffness matrix

The C++ Standard Library for Parallelism and Concurrency (HPX)

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

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