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A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Journal Article · · Journal of Peridynamics and Nonlocal Modeling
 [1];  [2];  [3];  [4];  [5]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Univ. of North Carolina, Charlotte, NC (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Univ. of Texas, Austin, TX (United States)
  5. Lehigh Univ., Bethlehem, PA (United States)
Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. Furthermore, we present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.
Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)
Grant/Contract Number:
AC05-00OR22725; NA0003525
OSTI ID:
1833985
Alternate ID(s):
OSTI ID: 1834348
Journal Information:
Journal of Peridynamics and Nonlocal Modeling, Journal Name: Journal of Peridynamics and Nonlocal Modeling Journal Issue: TBD Vol. TBD; ISSN 2522-896X
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

References (146)

On theL2 and theH1 couplings for an overlapping domain decomposition method using Lagrange multipliers journal January 2007
Heterogeneous coupling by virtual control methods journal December 2001
On the application of the Arlequin method to the coupling of particle and continuum models journal May 2008
Convergence of Peridynamics to Classical Elasticity Theory journal April 2008
Linearized Theory of Peridynamic States journal January 2010
Image Recovery via Nonlocal Operators journal August 2009
A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions journal August 2016
Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems journal February 2019
The peridynamic formulation for transient heat conduction journal September 2010
A coupled meshless finite point/Peridynamic method for 2D dynamic fracture analysis journal December 2016
The mechanically-based approach to 3D non-local linear elasticity theory: Long-range central interactions journal September 2010
A Morphing framework to couple non-local and local anisotropic continua journal May 2013
An enhanced coupling of PD grids to FE meshes journal September 2017
Eulerian derivation of the fractional advection–dispersion equation journal March 2001
Atomistic-to-continuum coupling journal April 2013
Application of a fractional advection-dispersion equation journal February 2000
Multiscaling fractional advection-dispersion equations and their solutions: MULTISCALING FRACTIONAL ADES journal January 2003
A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods journal May 2009
Peridynamics for multiscale materials modeling journal July 2008
The mechanically based non-local elasticity: an overview of main results and future challenges
  • Di Paola, Mario; Failla, Giuseppe; Pirrotta, Antonina
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 1993 https://doi.org/10.1098/rsta.2012.0433
journal June 2013
Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour journal July 2017
On the Coupling of Peridynamics With a Meshless Method Based on Classical Elasticity
  • Shojaei, Arman; Zaccariotto, Mirco; Galvanetto, Ugo
  • ASME 2016 International Mechanical Engineering Congress and Exposition, Volume 1: Advances in Aerospace Technology https://doi.org/10.1115/imece2016-65340
conference February 2017
Positive Definiteness of the Blended Force-Based Quasicontinuum Method journal January 2012
The Interface Control Domain Decomposition (ICDD) Method for Elliptic Problems journal January 2013
Nonlocal Theories in Continuum Mechanics journal January 2004
Peridynamics and Multiscale Modeling journal January 2011
Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending journal January 2015
Coupling of peridynamic theory and the finite element method journal January 2010
Variable horizon in a peridynamic medium journal January 2015
The Arlequin method as a flexible engineering design tool journal January 2005
Convergence, adaptive refinement, and scaling in 1D peridynamics
  • Bobaru, Florin; Yang, Mijia; Alves, Leonardo Frota
  • International Journal for Numerical Methods in Engineering, Vol. 77, Issue 6 https://doi.org/10.1002/nme.2439
journal February 2009
Bridging domain methods for coupled atomistic-continuum models with L 2 or H 1 couplings: BRIDGING DOMAIN METHODS journal September 2008
Ghost forces and spurious effects in atomic-to-continuum coupling methods by the Arlequin approach
  • Chamoin, Ludovic; Prudhomme, Serge; Ben Dhia, H.
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 8-9 https://doi.org/10.1002/nme.2879
journal August 2010
Coupling of nonlocal and local continuum models by the Arlequin approach: COUPLING OF NONLOCAL/LOCAL CONTINUUM MODELS BY THE ARLEQUIN APPROACH journal August 2011
Dual-horizon peridynamics: Dual-horizon peridynamics
  • Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang
  • International Journal for Numerical Methods in Engineering, Vol. 108, Issue 12 https://doi.org/10.1002/nme.5257
journal July 2016
Wave reflection and cut‐off frequencies in coupled FE‐peridynamic grids
  • Giannakeas, Ilias N.; Papathanasiou, Theodosios K.; Bahai, Hamid
  • International Journal for Numerical Methods in Engineering, Vol. 120, Issue 1 https://doi.org/10.1002/nme.6099
journal June 2019
Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations book January 2008
An accelerated domain decomposition procedure based on robin transmission conditions journal September 1997
The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture journal April 2014
Surface corrections for peridynamic models in elasticity and fracture journal August 2017
Superposition-based coupling of peridynamics and finite element method journal February 2019
Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness journal April 2020
Peridynamic States and Constitutive Modeling journal July 2007
Physically-Based Approach to the Mechanics of Strong Non-Local Linear Elasticity Theory journal August 2009
Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation journal December 2010
Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity journal November 2012
Nonlocal Constrained Value Problems for a Linear Peridynamic Navier Equation journal August 2013
Studies of dynamic crack propagation and crack branching with peridynamics journal January 2010
A finite difference-augmented peridynamics method for reducing wave dispersion journal October 2014
Why do cracks branch? A peridynamic investigation of dynamic brittle fracture journal November 2015
Superposition of non-ordinary state-based peridynamics and finite element method for material failure simulations journal December 2019
Mapped Displacement Discontinuity Method: Numerical Implementation and Analysis for Crack Problems journal February 2018
A Review of Benchmark Experiments for the Validation of Peridynamics Models journal February 2019
Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios journal April 2020
An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method journal March 1999
Reformulation of elasticity theory for discontinuities and long-range forces journal January 2000
Eulerian derivation of the fractional advection–dispersion equation journal March 2001
The random walk's guide to anomalous diffusion: a fractional dynamics approach journal December 2000
An optimization based domain decomposition method for partial differential equations journal May 1999
Problèmes mécaniques multi-échelles: la méthode Arlequin journal January 1998
Perspective on theories of non-Fickian transport in heterogeneous media journal May 2009
A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions journal June 2016
Convergence studies in meshfree peridynamic simulations journal June 2016
Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force journal September 2007
Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method journal July 2008
An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations journal May 2009
A coupling approach of discretized peridynamics with finite element method journal October 2012
Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains journal November 2013
Theory-based benchmarking of the blended force-based quasicontinuum method journal January 2014
A morphing approach to couple state-based peridynamics with classical continuum mechanics journal April 2016
Dual-horizon peridynamics: A stable solution to varying horizons journal May 2017
Coupling of FEM meshes with Peridynamic grids journal March 2018
Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model journal August 2018
A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations journal October 2018
A variable horizon method for coupling meshfree peridynamics to FEM journal October 2019
An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions journal July 2020
A force-based coupling scheme for peridynamics and classical elasticity journal January 2013
An energy-based coupling approach to nonlocal interface problems journal July 2020
A meshfree method based on the peridynamic model of solid mechanics journal June 2005
Combined finite element and peridynamic analyses for predicting failure in a stiffened composite curved panel with a central slot journal February 2012
Hybrid model of peridynamics and finite element method for static elastic deformation and brittle fracture analysis journal April 2020
An analytical study of wave propagation in a peridynamic bar with nonuniform discretization journal March 2018
Coupling approach of isogeometric analysis with non-ordinary state-based peridynamics journal July 2020
Peridynamics via finite element analysis journal November 2007
Fluid–structure partitioned procedures based on Robin transmission conditions journal July 2008
A peridynamic formulation of pressure driven convective fluid transport in porous media journal March 2014
A general peridynamics model for multiphase transport of non-Newtonian compressible fluids in porous media journal February 2020
nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications journal December 2020
Kinetics of phase transformations in the peridynamic formulation of continuum mechanics journal September 2006
A morphing strategy to couple non-local to local continuum mechanics journal June 2012
An effective way to couple FEM meshes and Peridynamics grids for the solution of static equilibrium problems journal September 2016
Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method journal February 2021
Coupling of peridynamics with finite elements for brittle crack propagation problems journal June 2020
A coupling model of XFEM/peridynamics for 2D dynamic crack propagation and branching problems journal August 2020
The bond-based peridynamic system with Dirichlet-type volume constraint journal January 2014
Atomistic-to-continuum coupling journal April 2013
Application of a fractional advection-dispersion equation journal February 2000
Multiscaling fractional advection-dispersion equations and their solutions: MULTISCALING FRACTIONAL ADES journal January 2003
An asymptotically compatible approach for Neumann-type boundary condition on nonlocal problems journal June 2020
Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress journal November 2002
Coupling of FEM and ordinary state-based peridynamics for brittle failure analysis in 3D journal April 2019
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics journal July 2004
Atomistic/continuum coupling in computational materials science journal April 2003
Regularity theory for parabolic nonlinear integral operators journal March 2011
75 Years of Mathematics of Computation book January 2020
Matching conditions in the quasicontinuum method: Removal of the error introduced at the interface between the coarse-grained and fully atomistic region journal June 2004
Uniform accuracy of the quasicontinuum method journal December 2006
Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour journal July 2017
Drop-Shock Failure Prediction in Electronic Packages by Using Peridynamic Theory journal March 2012
Meshfree and particle methods and their applications journal January 2002
On the Coupling of Peridynamics With a Meshless Method Based on Classical Elasticity
  • Shojaei, Arman; Zaccariotto, Mirco; Galvanetto, Ugo
  • ASME 2016 International Mechanical Engineering Congress and Exposition, Volume 1: Advances in Aerospace Technology https://doi.org/10.1115/IMECE2016-65340
conference February 2017
Robin–Robin Domain Decomposition Methods for the Stokes–Darcy Coupling journal January 2007
Nonlocal Linear Image Regularization and Supervised Segmentation journal January 2007
On Atomistic-to-Continuum Coupling by Blending journal January 2008
A Parallel Robin–Robin Domain Decomposition Method for the Stokes–Darcy System journal January 2011
A Nonlocal Vector Calculus with Application to Nonlocal Boundary Value Problems journal January 2010
Image Denoising Methods. A New Nonlocal Principle journal January 2010
Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions journal July 2011
Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints journal January 2012
Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations journal January 2013
An Optimization-based Atomistic-to-Continuum Coupling Method journal January 2014
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models journal January 2014
A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension journal January 2016
Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization journal January 2017
Quasi-nonlocal Coupling of Nonlocal Diffusions journal January 2017
A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models journal January 2018
Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling journal January 2019
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints journal January 2020
Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models journal January 2020
Optimization Based Nonoverlapping Domain Decomposition Algorithms and Their Convergence journal January 2001
An Optimization-Based Domain Decomposition Method for the Navier--Stokes Equations journal January 2000
A Gradient Method Approach to Optimization-Based Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms journal January 2000
The exit-time problem for a Markov jump process journal December 2014
A Nonlocal Vector Calculus, Nonlocal Volume-Constrained Problems, and Nonlocal Balance laws journal January 2013
A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems journal June 2021
Formulation of symmetry boundary modeling in non-ordinary state-based peridynamics and coupling with finite element analysis journal June 2017
Handbook of Peridynamic Modeling book October 2016
Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes journal October 2017
Optimization–Based Coupling of Nonlocal and Local Diffusion Models journal January 2015
Adaptive Refinement and Multiscale Modeling in 2d Peridynamics journal January 2011
Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending journal January 2015
A Force-Based Blending Model forAtomistic-to-Continuum Coupling journal January 2007
Peridynamic Augmented XFEM conference January 2017
The Multi-Horizon Peridynamics journal January 2019
Analysis of a scalar nonlocal peridynamic model with a sign changing kernel journal January 2013
Bridging Methods for Atomistic-to-continuum Coupling and Their Implementation journal June 2010

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