A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

Ren, Bo; Wu, C. T.; Seleson, Pablo D.; Zeng, Danielle; Lyu, Dandan

doi:10.1007/s10704-018-0317-4

Title: A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

Abstract

Here, this paper presents a discontinuous Galerkin weak form for bond-based peridynamic models to predict the damage of fiber-reinforced composite laminates. To represent the anisotropy of a laminate in a peridynamic model, a lamina is simplified as a transversely isotropic medium under a plane stress condition. The laminated structure is modeled by stacking the surface mesh layers along the thickness direction according to the laminate sequence. To avoid a mesh dependence on either the fiber orientation or the discretization, the spherical harmonic expansion theory is employed to construct a function for the micro-elastic modulus in terms of the bond-fiber angle. The laminate material is decomposed into an isotropic matrix material part and a transversely isotropic material part. The bond stiffness can be evaluated using the engineering material constants, based on the equivalence between the elastic energy density in the peridynamic theory and the elastic energy density in the classic continuum mechanics theory. Benchmark tests are conducted to verify the proposed model. Numerical results illustrate that the convergence of simulations with different horizon sizes and meshes can be achieved. In terms of damage analysis, the proposed model can capture the dynamic process of the complex coupling of the inner-layer and delaminationmore » damage modes.« less

Authors:

Ren, Bo ^[1]; Wu, C. T. ^[1];

^[2]; Zeng, Danielle ^[3]; Lyu, Dandan ^[4]

Livermore Software Technology Corporation, Livermore, CA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
Ford Motor Company, Ford Research and Innovation Center, Dearborn, MI (United States)
Univ. of California, Berkeley, CA (United States). Department of Civil and Environmental Engineering

Publication Date:: Thu Oct 04 00:00:00 EDT 2018

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1479710

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: International Journal of Fracture

Additional Journal Information:: Journal Volume: 214; Journal Issue: 1; Journal ID: ISSN 0376-9429

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; Peridynamic theory; Finite element method; Failure analysis; Discontinuous Galerkin method; Fiber-reinforced composites

Citation Formats


                    Ren, Bo, Wu, C. T., Seleson, Pablo D., Zeng, Danielle, and Lyu, Dandan. A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations.  United States: N. p., 2018. 
Web.  doi:10.1007/s10704-018-0317-4.

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                    Ren, Bo, Wu, C. T., Seleson, Pablo D., Zeng, Danielle, & Lyu, Dandan. A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations.  United States.  https://doi.org/10.1007/s10704-018-0317-4

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                    Ren, Bo, Wu, C. T., Seleson, Pablo D., Zeng, Danielle, and Lyu, Dandan. Thu .  
"A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations".  United States.  https://doi.org/10.1007/s10704-018-0317-4.  https://www.osti.gov/servlets/purl/1479710.

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@article{osti_1479710,

  title        = {A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations},

  author       = {Ren, Bo and Wu, C. T. and Seleson, Pablo D. and Zeng, Danielle and Lyu, Dandan},

  abstractNote = {Here, this paper presents a discontinuous Galerkin weak form for bond-based peridynamic models to predict the damage of fiber-reinforced composite laminates. To represent the anisotropy of a laminate in a peridynamic model, a lamina is simplified as a transversely isotropic medium under a plane stress condition. The laminated structure is modeled by stacking the surface mesh layers along the thickness direction according to the laminate sequence. To avoid a mesh dependence on either the fiber orientation or the discretization, the spherical harmonic expansion theory is employed to construct a function for the micro-elastic modulus in terms of the bond-fiber angle. The laminate material is decomposed into an isotropic matrix material part and a transversely isotropic material part. The bond stiffness can be evaluated using the engineering material constants, based on the equivalence between the elastic energy density in the peridynamic theory and the elastic energy density in the classic continuum mechanics theory. Benchmark tests are conducted to verify the proposed model. Numerical results illustrate that the convergence of simulations with different horizon sizes and meshes can be achieved. In terms of damage analysis, the proposed model can capture the dynamic process of the complex coupling of the inner-layer and delamination damage modes.},

  doi          = {10.1007/s10704-018-0317-4},

  journal      = {International Journal of Fracture},

  number       = 1,

  volume       = 214,

  place        = {United States},

  year         = {Thu Oct 04 00:00:00 EDT 2018},

  month        = {Thu Oct 04 00:00:00 EDT 2018}

}

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https://doi.org/10.1007/s10704-018-0317-4

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Cited by: 14 works

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Fig. 1: The fiber orientation in a lamina.

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Works referenced in this record:

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Title: A peridynamic failure analysis of fiber-reinforced composite laminates using finite element discontinuous Galerkin approximations

Abstract

Citation Formats

Figures / Tables:

A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media journal, July 2014

Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials journal, July 2016

A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis journal, January 2017

A finite element method for crack growth without remeshing journal, September 1999

A morphing approach to couple state-based peridynamics with classical continuum mechanics journal, April 2016

Convergence studies in meshfree peridynamic simulations journal, June 2016

Peridynamic modeling of concrete structures journal, July 2007

On the role of the Influence Function in the Peridynamic Theory journal, January 2011

Peridynamic analytical method for progressive damage in notched composite laminates journal, February 2014

Peridynamic States and Constitutive Modeling journal, July 2007

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

A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process journal, July 2015

Force flux and the peridynamic stress tensor journal, April 2008

Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites journal, April 2012

Continuous and discontinuous finite element methods for a peridynamics model of mechanics journal, February 2011

Peridynamic modeling of delamination growth in composite laminates journal, November 2015

Peridynamic Theory and Its Applications book, January 2014

Numerical simulations of fast crack growth in brittle solids journal, September 1994

The Meaning, Selection, and Use of the Peridynamic Horizon and its Relation to Crack Branching in Brittle Materials journal, June 2012

Modeling Dynamic Fracture and Damage in a Fiber-Reinforced Composite Lamina with Peridynamics journal, January 2011

A three-dimensional impact-penetration algorithm with erosion journal, January 1987

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

Modeling and simulation of large-scale ductile fracture in plates and shells journal, September 2012

The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture journal, April 2014

A meshfree continuous–discontinuous approach for the ductile fracture modeling in explicit dynamics analysis journal, May 2016

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

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

Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions journal, January 1987

Peridynamic Analysis of Impact Damage in Composite Laminates journal, July 2008

Peridynamics simulations of geomaterial fragmentation by impulse loads: Peridynamics simulations of geomaterial fragmentation by impulse loads journal, March 2015

Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence journal, October 2016

Regularization of material instabilities by meshfree approximations with intrinsic length scales journal, March 2000

Analysis of Brazed Single-Lap Joints Using the Peridynamics Theory conference, June 2012

A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media
journal, July 2014

Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials
journal, July 2016

A 3D discontinuous Galerkin finite element method with the bond-based peridynamics model for dynamic brittle failure analysis
journal, January 2017

A finite element method for crack growth without remeshing
journal, September 1999

A morphing approach to couple state-based peridynamics with classical continuum mechanics
journal, April 2016

Convergence studies in meshfree peridynamic simulations
journal, June 2016

Peridynamic modeling of concrete structures
journal, July 2007

On the role of the Influence Function in the Peridynamic Theory
journal, January 2011

Peridynamic analytical method for progressive damage in notched composite laminates
journal, February 2014

Peridynamic States and Constitutive Modeling
journal, July 2007

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

A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process
journal, July 2015

Force flux and the peridynamic stress tensor
journal, April 2008

Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites
journal, April 2012

Continuous and discontinuous finite element methods for a peridynamics model of mechanics
journal, February 2011

Peridynamic modeling of delamination growth in composite laminates
journal, November 2015

Peridynamic Theory and Its Applications
book, January 2014

Numerical simulations of fast crack growth in brittle solids
journal, September 1994

The Meaning, Selection, and Use of the Peridynamic Horizon and its Relation to Crack Branching in Brittle Materials
journal, June 2012

Modeling Dynamic Fracture and Damage in a Fiber-Reinforced Composite Lamina with Peridynamics
journal, January 2011

A three-dimensional impact-penetration algorithm with erosion
journal, January 1987

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

Modeling and simulation of large-scale ductile fracture in plates and shells
journal, September 2012

The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture
journal, April 2014

A meshfree continuous–discontinuous approach for the ductile fracture modeling in explicit dynamics analysis
journal, May 2016

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

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

Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions
journal, January 1987

Peridynamic Analysis of Impact Damage in Composite Laminates
journal, July 2008

Peridynamics simulations of geomaterial fragmentation by impulse loads: Peridynamics simulations of geomaterial fragmentation by impulse loads
journal, March 2015

Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence
journal, October 2016

Regularization of material instabilities by meshfree approximations with intrinsic length scales
journal, March 2000

Analysis of Brazed Single-Lap Joints Using the Peridynamics Theory
conference, June 2012