Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations

Seleson, Pablo

doi:10.1016/j.cma.2014.06.016

Cited by 147 publications

(109 citation statements)

References 40 publications

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“…The accuracy of both methods is similar. There exist more accurate quadrature rules, which are discussed in Bobaru and Duangpanya (2012), Seleson (2014). A comparison of combinations of different surface correction methods and quadrature rules is left for future work.…”

Section: Discussionmentioning

confidence: 98%

“…The third column is the Young's modulus obtained with the PA-HHB volume correction. Here, the error is very (Bobaru and Duangpanya 2012;Seleson 2014), but considering all of them as well is beyond the scope of this paper. One reason for the similar accuracies of the quadrature rules in Table 2 is that the surface effect of peridynamics affects the computation of the Young's modulus using the stress-strain curve.…”

Section: Verification Of the Constitutive Lawmentioning

confidence: 96%

“…For a suitable implementation of the piecewise constant approximation of the integrals we define the integration domain as all volumes touched by the radial cutoff δ. More accurate quadrature rules are discussed in Bobaru and Duangpanya (2012), Seleson (2014) enon is the so-called skin effect (Hu et al 2012), and different surface correction methods (Kilic and Madenci 2010;Liu and Hong 2012;Macek and Silling 2007) exists. One can show that the IPMB model is a special case of the Linear Peridynamic Solid (LPS) statebased model ) for a single-point collocation quadrature rule, the Poisson ratio ν := 1 4 and the micro potential ω = 1 X j −X i .…”

Section: Discretizationmentioning

confidence: 99%

“…Note that here the same spatial algorithm of LAMMPS is used and that the accuracy is influenced by the volume corrections discussed in Seleson (2014). Table 1 shows the range of the parameters that define the parametric input space used in the simulations.…”

Section: Model Problemmentioning

confidence: 99%

“…The error with respect to the classical theory is ≈ 0.05 for the spatial integration of LAMMPS. Next we focus on more accurate quadrature rules (Seleson 2014), e.g. the PA-HHB partial volume correction (Hu et al 2010).…”

Section: Verification Of the Constitutive Lawmentioning

confidence: 99%

See 4 more Smart Citations

Bond-based peridynamics: a quantitative study of Mode I crack opening

Diehl¹,

Franzelin²,

Pflüger³

et al. 2016

Int J Fract

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This paper shows a new approach to estimate the critical traction for Mode I crack opening before crack growth by numerical simulation. For quasi-static loading, Linear Elastic Fracture Mechanics predicts the critical traction before crack growth. To simulate the crack growth, we used bond-based peridynamics, a non-local generalization of continuum mechanics. We discretize the peridynamics equation of motion with a collocation by space approach, the socalled EMU nodal discretization. As the constitutive law, we employ the improved prototype micro brittle material model. This bond-based material model is verified by the Young's modulus from classical theory for a homogeneous deformation for different quadrature rules. For the EMU-ND we studied the behavior for different ratios of the horizon and nodal spacing to gain a robust value for a large variety of materials. To access this wide range of materials, we applied sparse grids, a technique to build high-dimensional surrogate models. Sparse grids significantly reduce the number of simulation runs compared to a full grid approach and keep up a similar approximation accuracy. For the validation of the quasi-static loading process, we show that the critical traction is independent of the material density for most material parameters. The bond-based IPMB model with EMU nodal discretization seems very robust for the ratio δ/ΔX = 3 for a wide range of materials, if an error of 5 % is acceptable.

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Section: Discussionmentioning

confidence: 98%

Section: Verification Of the Constitutive Lawmentioning

confidence: 96%

Section: Discretizationmentioning

confidence: 99%

Section: Model Problemmentioning

confidence: 99%

Section: Verification Of the Constitutive Lawmentioning

confidence: 99%

See 3 more Smart Citations

Bond-based peridynamics: a quantitative study of Mode I crack opening

Diehl¹,

Franzelin²,

Pflüger³

et al. 2016

Int J Fract

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Linearized state‐based peridynamics for 2‐D problems

Sarego

Bobaru

et al. 2016

Numerical Meth Engineering

109

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Summary In this work, the authors formulate a 2‐D linearized ordinary state‐based peridynamic model of elastic deformations and compute the stiffness matrix for 2‐D plane stress/strain conditions. This model is then verified by testing the recovery of elastic properties for given Poisson's ratios in the range 0.1–0.45. The convergence behavior of peridynamic solutions in terms of the size of the nonlocal region by comparison with the classical (local) mechanics model is also discussed. The degree to which the peridynamic surface effect influences the recovery of elastic properties is examined, and stress/strain recovery values are found to have a definite influence on the results. The technique used here can provide the basis for applying 2‐D peridynamic models to the study of fatigue failure and quasi‐static fracture problems. Copyright © 2016 John Wiley & Sons, Ltd.

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The boundary element method of peridynamics

Xue

Wang

et al. 2021

Numerical Meth Engineering

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The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and nonlocality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems. Some important issues attract much attention, such as the computation of infinite domains, the treatment of softening of boundaries due to an incomplete horizon, and time accumulation error in dynamic processes. In this work, we develop the boundary element method of peridynamics (PD-BEM). The numerical examples demonstrate that the PD-BEM exhibits several features. First, for nondestructive cases, the PD-BEM can be one to two orders of magnitude faster than the meshless particle method of peridynamics (PD-MPM) that directly discretizes the computational domains; second, it eliminates the time accumulation error, and thus conserves the total energy much better than the PD-MPM; third, it does not exhibit spurious boundary softening phenomena. For destructive cases where new boundaries emerge during the loading process, we propose a coupling scheme where the PD-MPM is applied to the cracked region and the PD-BEM is applied to the uncracked region such that the time of computation can be significantly reduced.

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Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations

Cited by 147 publications

References 40 publications

Bond-based peridynamics: a quantitative study of Mode I crack opening

Bond-based peridynamics: a quantitative study of Mode I crack opening

Linearized state‐based peridynamics for 2‐D problems

The boundary element method of peridynamics

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