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

Diehl, Patrick; Lipton, Robert; Wick, Thomas; Tyagi, Mayank

doi:10.31224/osf.io/gty2b

Cited by 11 publications

(4 citation statements)

References 303 publications

(473 reference statements)

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“…because it has no restriction on the Poisson ratio, ensures stable computing, and is the most widely used of the three forms in engineering [15,[17][18][19][20][21].…”

Section: Fundamentals Of Pdmentioning

confidence: 99%

An updated fast continuous contact detection algorithm and its implementation in case study of ice-structure interaction by peridynamics

Zhang

Tao

et al. 2023

Marine Structures

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“…because it has no restriction on the Poisson ratio, ensures stable computing, and is the most widely used of the three forms in engineering [15,[17][18][19][20][21].…”

Section: Fundamentals Of Pdmentioning

confidence: 99%

An updated fast continuous contact detection algorithm and its implementation in case study of ice-structure interaction by peridynamics

Zhang

Tao

et al. 2023

Marine Structures

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“…Specifically, this challenge aims at evaluating the computational ability to predict crack initiation and propagation of ductile fracture with respect to experimental observations. A recent comparative literature overview was conducted in [123]. As reported in [72], standard phase-field formulations without estimating [72] accurate ductile material properties quantitatively overestimate the post-yielding load-displacement response, which can be improved by performing an accurate calibration of the plasticity and phase-field parameters.…”

Section: Example 4: Sandia Fracture Challengementioning

confidence: 99%

Bayesian inversion for unified ductile phase-field fracture

et al. 2021

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The prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the $$\hat{R}{-}convergence$$ R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

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“…The formulation successfully captures qualitative features seen in a range of experiments [22]. As of this writing it appears that only a few quasi static PD simulations are available [21,32,53,72,69,7,39,57,25]. For quasi static problems there is no inertia and time is represented by a load parameter.…”

Section: Introductionmentioning

confidence: 95%

Quasistatic Fracture using Nonlinear-Nonlocal Elastostatics with Explicit Tangent Stiffness Matrix

Diehl¹,

Lipton²

2022

Preprint

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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 (RNP) potential in a peridynamic formulation. The potential function is given by an explicit formula with and 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 {\it soft loading} (load in force) and {\it hard loading} (load in displacement). 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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A comparative review of peridynamics and phase-field models for engineering fracture mechanics

Cited by 11 publications

References 303 publications

An updated fast continuous contact detection algorithm and its implementation in case study of ice-structure interaction by peridynamics

An updated fast continuous contact detection algorithm and its implementation in case study of ice-structure interaction by peridynamics

Bayesian inversion for unified ductile phase-field fracture

Quasistatic Fracture using Nonlinear-Nonlocal Elastostatics with Explicit Tangent Stiffness Matrix

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