Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending

Seleson, Pablo; Ha, Youn Doh; Beneddine, Samir

doi:10.1615/intjmultcompeng.2014011338

Cited by 71 publications

(44 citation statements)

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“…Aside from the pure PD formulation above mentioned, much work was devoted to the coupling of peridynamics with the continuum methods [7,8,[22][23][24]. Such strategies enable to model the fracture domain with PD while other domain modeled with continuum methods.…”

Section: Introductionmentioning

confidence: 99%

“…NOSB-PD is capable of simulating the material with advanced constitute models, e.g. viscoplasticity model [20], the Drucker-Prager plasticity model [10] and Johnson-Cook (JC) constitutive model [21].Aside from the pure PD formulation above mentioned, much work was devoted to the coupling of peridynamics with the continuum methods [7,8,[22][23][24]. Such strategies enable to model the fracture domain with PD while other domain modeled with continuum methods.…”

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confidence: 99%

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Dual-horizon peridynamics: A stable solution to varying horizons

Ren

Zhuang

Rabczuk

2017

Computer Methods in Applied Mechanics and Engineering

555

105

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In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.Comment: 21 page

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Dual-horizon peridynamics: A stable solution to varying horizons

Ren

Zhuang

Rabczuk

2017

Computer Methods in Applied Mechanics and Engineering

555

105

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“…Therefore, the leading term contributing to the truncation error is the one containing fourth partial derivatives of the displacement field, giving the O(δ 2 ) error in (3.5). We observe that [55]…”

Section: )mentioning

confidence: 89%

“…It has been proven to provide exact solutions to a certain class of equilibrium problems, and numerical experiments have demonstrated its viability for model coupling within a computational simulation. A second result is the formulation of a blendingbased coupling approach [55,2] that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Strong Local-Nonlocal Coupling for Integrated Fracture Modeling

Littlewood

Silling

Mitchell

et al. 2015

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Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is employed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Integrated Fracture Modeling," completed within the Computing and Information Sciences (CIS) Investment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves convergence behavior. Finally, a novel approach for modeling ductile failure has been developed, motivated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software implementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.

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“…Recently, some coupling schemes have been proposed to combine CCM and BPD models; for example, the variable horizon method [13,19], the force-based coupling method [17,18], the Arlequin coupling method [10] and the morphing method [14]. The variable horizon method blends the local and nonlocal equations by reduction of the peri -1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 dynamic horizon in the vicinity of the nonlocal model interface where the mathematical incompatibility is greatly reduced.…”

Section: Introductionmentioning

confidence: 99%

A morphing approach to couple state-based peridynamics with classical continuum mechanics

Han

Lubineau

Azdoud

et al. 2016

Computer Methods in Applied Mechanics and Engineering

137

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Please cite this article as: F. Han, G. Lubineau, Y. Azdoud, A. Askari, A morphing approach to couple state-based peridynamics with classical continuum mechanics, Comput. Methods Appl. Mech. Engrg. (2015), http://dx.doi. org/10.1016/j.cma.2015.12.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

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Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending

Cited by 71 publications

References 0 publications

Dual-horizon peridynamics: A stable solution to varying horizons

Dual-horizon peridynamics: A stable solution to varying horizons

Strong Local-Nonlocal Coupling for Integrated Fracture Modeling

A morphing approach to couple state-based peridynamics with classical continuum mechanics

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