Enabling fast, stable and accurate peridynamic computations using multi-time-step integration

Lindsay, P.; Parks, M. L.; Prakash, A.

doi:10.1016/j.cma.2016.03.049

Title: Enabling fast, stable and accurate peridynamic computations using multi-time-step integration

Abstract

Peridynamics is a nonlocal extension of classical continuum mechanics that is well-suited for solving problems with discontinuities such as cracks. This paper extends the peridynamic formulation to decompose a problem domain into a number of smaller overlapping subdomains and to enable the use of different time steps in different subdomains. This approach allows regions of interest to be isolated and solved at a small time step for increased accuracy while the rest of the problem domain can be solved at a larger time step for greater computational efficiency. Lastly, performance of the proposed method in terms of stability, accuracy, and computational cost is examined and several numerical examples are presented to corroborate the findings.

Authors:

Lindsay, P. ^[1]; Parks, M. L. ^[2];

^[1]

Lyles School of Civil Engineering, West Lafayette, IN (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Publication Date:: Wed Apr 13 00:00:00 EDT 2016

Research Org.:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1263548

Alternate Identifier(s):: OSTI ID: 1365589

Report Number(s):: SAND-2015-8053J
Journal ID: ISSN 0045-7825; PII: S0045782516301360

Grant/Contract Number:: AC04-94AL85000; FC02-12ER26104; SC0008629

Resource Type:: Accepted Manuscript

Journal Name:: Computer Methods in Applied Mechanics and Engineering

Additional Journal Information:: Journal Volume: 306; Journal Issue: C; Journal ID: ISSN 0045-7825

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; peridynamics; multi-time-step; nonlocal; fracture

Citation Formats


                    Lindsay, P., Parks, M. L., and Prakash, A. Enabling fast, stable and accurate peridynamic computations using multi-time-step integration.  United States: N. p., 2016. 
Web.  doi:10.1016/j.cma.2016.03.049.

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                    Lindsay, P., Parks, M. L., & Prakash, A. Enabling fast, stable and accurate peridynamic computations using multi-time-step integration.  United States.  https://doi.org/10.1016/j.cma.2016.03.049

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                    Lindsay, P., Parks, M. L., and Prakash, A. Wed .  
"Enabling fast, stable and accurate peridynamic computations using multi-time-step integration".  United States.  https://doi.org/10.1016/j.cma.2016.03.049.  https://www.osti.gov/servlets/purl/1263548.

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@article{osti_1263548,

  title        = {Enabling fast, stable and accurate peridynamic computations using multi-time-step integration},

  author       = {Lindsay, P. and Parks, M. L. and Prakash, A.},

  abstractNote = {Peridynamics is a nonlocal extension of classical continuum mechanics that is well-suited for solving problems with discontinuities such as cracks. This paper extends the peridynamic formulation to decompose a problem domain into a number of smaller overlapping subdomains and to enable the use of different time steps in different subdomains. This approach allows regions of interest to be isolated and solved at a small time step for increased accuracy while the rest of the problem domain can be solved at a larger time step for greater computational efficiency. Lastly, performance of the proposed method in terms of stability, accuracy, and computational cost is examined and several numerical examples are presented to corroborate the findings.},

  doi          = {10.1016/j.cma.2016.03.049},

  journal      = {Computer Methods in Applied Mechanics and Engineering},

  number       = C,

  volume       = 306,

  place        = {United States},

  year         = {Wed Apr 13 00:00:00 EDT 2016},

  month        = {Wed Apr 13 00:00:00 EDT 2016}

}

Copy to clipboard

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https://doi.org/10.1016/j.cma.2016.03.049

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Works referencing / citing this record:

Superposition-based coupling of peridynamics and finite element method
journal, February 2019

Sun, Wei; Fish, Jacob
Computational Mechanics, Vol. 64, Issue 1
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Title: Enabling fast, stable and accurate peridynamic computations using multi-time-step integration

Abstract

Citation Formats

Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review journal, February 2003

A survey of the extended finite element journal, June 2008

Elastic crack growth in finite elements with minimal remeshing journal, June 1999

The design and analysis of the Generalized Finite Element Method journal, January 2000

An h-p adaptive method using clouds journal, December 1996

The partition of unity finite element method: Basic theory and applications journal, December 1996

The cohesive zone model: advantages, limitations and challenges journal, January 2002

Element-free Galerkin methods journal, January 1994

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments journal, February 2010

Reproducing kernel particle methods for structural dynamics journal, May 1995

Elasticity theory of materials with long range cohesive forces journal, September 1967

Reformulation of elasticity theory for discontinuities and long-range forces journal, January 2000

Peridynamic States and Constitutive Modeling journal, July 2007

A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics journal, January 2004

Computationally efficient multi-time-step method for partitioned time integration of highly nonlinear structural dynamics journal, March 2014

Peridynamic Theory of Solid Mechanics book, September 2010

Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach journal, June 2007

Peridynamic State-Based Models and the Embedded-Atom Model journal, January 2014

Peridynamics as an Upscaling of Molecular Dynamics journal, January 2009

Peridynamic modeling of concrete structures journal, July 2007

A meshfree method based on the peridynamic model of solid mechanics journal, June 2005

Deformation of a Peridynamic Bar journal, December 2003

Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations journal, December 2014

A Method of Computation for Structural Dynamics journal, July 1959

A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters journal, January 1982

Partitioned analysis of coupled mechanical systems journal, March 2001

Staggered transient analysis procedures for coupled mechanical systems: Formulation journal, October 1980

Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity journal, March 2006

Mixed methods for time integration journal, February 1979

Stability of explicit-implicit mesh partitions in time integration journal, January 1978

Mixed-time implicit-explicit finite elements for transient analysis journal, January 1982

Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems journal, January 1989

Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory journal, June 1978

Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples journal, June 1978

An explicit multi-time step integration method for second order equations journal, January 1992

Stability analysis of a multi-time step explicit integration method journal, March 1992

The subcycled Newmark algorithm journal, August 1997

A study of the stability of subcycling algorithms in structural dynamics journal, April 1998

A partial velocity approach to subcycling structural dynamics journal, January 2003

A concurrent explicit-implicit algorithm in structural dynamics journal, April 1994

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics journal, June 1994

A scalable Lagrange multiplier based domain decomposition method for time-dependent problems journal, November 1995

Multi-time-step explicit-implicit method for non-linear structural dynamics journal, January 2000

A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis journal, January 2002

A multiscale extended finite element method for crack propagation journal, January 2008

A two-scale approach with homogenization for the computation of cracked structures journal, September 2007

Substructuring FE–XFE approaches applied to three-dimensional crack propagation journal, June 2008

A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures journal, January 2007

A bridging domain method for coupling continua with molecular dynamics journal, May 2004

Domain decomposition techniques for the efficient modeling of brittle heterogeneous materials journal, March 2011

A coupled finite element-element-free Galerkin method journal, January 1995

Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains journal, November 2013

Superposition-based coupling of peridynamics and finite element method journal, February 2019

Voronoi-based peridynamics and cracking analysis with adaptive refinement: Voronoi-based peridynamics and cracking analysis with adaptive refinement journal, August 2017

Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review
journal, February 2003

A survey of the extended finite element
journal, June 2008

Elastic crack growth in finite elements with minimal remeshing
journal, June 1999

The design and analysis of the Generalized Finite Element Method
journal, January 2000

An h-p adaptive method using clouds
journal, December 1996

The partition of unity finite element method: Basic theory and applications
journal, December 1996

The cohesive zone model: advantages, limitations and challenges
journal, January 2002

Element-free Galerkin methods
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Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments
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Reproducing kernel particle methods for structural dynamics
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Elasticity theory of materials with long range cohesive forces
journal, September 1967

Reformulation of elasticity theory for discontinuities and long-range forces
journal, January 2000

Peridynamic States and Constitutive Modeling
journal, July 2007

A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics
journal, January 2004

Computationally efficient multi-time-step method for partitioned time integration of highly nonlinear structural dynamics
journal, March 2014

Peridynamic Theory of Solid Mechanics
book, September 2010

Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach
journal, June 2007

Peridynamic State-Based Models and the Embedded-Atom Model
journal, January 2014

Peridynamics as an Upscaling of Molecular Dynamics
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Peridynamic modeling of concrete structures
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journal, December 2014

A Method of Computation for Structural Dynamics
journal, July 1959

A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters
journal, January 1982

Partitioned analysis of coupled mechanical systems
journal, March 2001

Staggered transient analysis procedures for coupled mechanical systems: Formulation
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journal, March 2006

Mixed methods for time integration
journal, February 1979

Stability of explicit-implicit mesh partitions in time integration
journal, January 1978

Mixed-time implicit-explicit finite elements for transient analysis
journal, January 1982

Explicit-explicit subcycling with non-integer time step ratios for structural dynamic systems
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Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory
journal, June 1978

Implicit-Explicit Finite Elements in Transient Analysis: Implementation and Numerical Examples
journal, June 1978

An explicit multi-time step integration method for second order equations
journal, January 1992

Stability analysis of a multi-time step explicit integration method
journal, March 1992

The subcycled Newmark algorithm
journal, August 1997

A study of the stability of subcycling algorithms in structural dynamics
journal, April 1998

A partial velocity approach to subcycling structural dynamics
journal, January 2003

A concurrent explicit-implicit algorithm in structural dynamics
journal, April 1994

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics
journal, June 1994

A scalable Lagrange multiplier based domain decomposition method for time-dependent problems
journal, November 1995

Multi-time-step explicit-implicit method for non-linear structural dynamics
journal, January 2000

A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis
journal, January 2002

A multiscale extended finite element method for crack propagation
journal, January 2008

A two-scale approach with homogenization for the computation of cracked structures
journal, September 2007

Substructuring FE–XFE approaches applied to three-dimensional crack propagation
journal, June 2008

A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures
journal, January 2007

A bridging domain method for coupling continua with molecular dynamics
journal, May 2004

Domain decomposition techniques for the efficient modeling of brittle heterogeneous materials
journal, March 2011

A coupled finite element-element-free Galerkin method
journal, January 1995

Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains
journal, November 2013

Superposition-based coupling of peridynamics and finite element method
journal, February 2019

Voronoi-based peridynamics and cracking analysis with adaptive refinement: Voronoi-based peridynamics and cracking analysis with adaptive refinement
journal, August 2017