Elastic vortices and thermally-driven cracks in brittle materials with peridynamics

Xu, Zhanping; Zhang, Guanfeng; Chen, Ziguang; Bobaru, Florin

doi:10.1007/s10704-017-0256-5

Cited by 72 publications

(28 citation statements)

References 37 publications

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“…Physical features in damage (evolving cracks and distributed failure) and small-scale heterogeneities can be naturally modeled using nonlocal approaches [11,12], and would be otherwise difficult to describe or prohibitively expensive to compute with classical local approaches. Peridynamics, as a nonlocal extension of continuum mechanics [13,14], has been successful in modeling damage evolution and material failure [15,16,13]. Dynamic brittle fracture [17][18][19], fatigue and thermallyinduced cracking [20,16], fracture in porous and granular materials [21][22][23], failure of composites [24,25], corrosion damage [26][27][28][29], and stress corrosion cracking [30][31][32], are among some applications of this formulation in modeling material damage.…”

Section: Introductionmentioning

confidence: 99%

Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

Jafarzadeh

Larios

Bobaru

2020

J Peridyn Nonlocal Model

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We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier space, resulting in computations that scale as ( log ). The limitation of regular spectral methods to periodic problems is eliminated using the volume penalization method. We show that arbitrary boundary conditions or volume constraints can be enforced in this way to achieve high levels of accuracy. To test the performance of our approach we compare the computational results with analytical solutions of the nonlocal problem. The performance is tested with convergence studies in terms of nodal discretization and the size of the penalization parameter in problems with Dirichlet and Neumann boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

Jafarzadeh

Larios

Bobaru

2020

J Peridyn Nonlocal Model

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“…(8) via the energy minimization method, using the nonlinear conjugate gradient (NCG) method with secant line search. The detail of the algorithm can be found in [32,35]. Instead of the Polak-Ribiere formula [72], we use the hybrid Hu-Storey (HuS) formula [73], for a faster convergence.…”

Section: Numerical Discretizationmentioning

confidence: 99%

“…Peridynamics (PD) is a nonlocal theory which has received considerable attention since its introduction almost two decades ago [25,26]. PD reformulates the classical continuum mechanics by eliminating spatial derivatives to model mechanical [27][28][29][30][31][32][33][34][35][36][37], diffusion/corrosion [38][39][40][41][42][43], or mechano-chemical [44][45][46] etc., behaviors in materials involving damage. Using spatial integration rather than differentiation leads to a mathematically consistent formulation that works naturally for problems in which discontinuities in the domain (such as cracks) appear.…”

Section: Introductionmentioning

confidence: 99%

A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete

Zhao

Chen

Mehrmashhadi

et al. 2020

Engineering Fracture Mechanics

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Concrete fracture caused by corrosion of reinforcing bars may cause subsequent structure failure. To better predict this process, we introduce a partially-homogenized stochastic peridynamic model with the simplest constitutive relation (linear elastic with brittle failure). The model links microscale information (phase volume fractions of mortar, aggregates, interfaces) to macroscale fracture behavior, while costing the same as a fully homogenized model. We show, and explain why a fully-homogenized peridynamic model fails to capture the correct concrete fracture modes/patterns, while the new model succeeds. The multiscale model predicts the evolution of fracture in reinforced concrete caused by corrosion products expansion in samples with a single or multiple rebars. Non-uniform expansion of corrosion products is enforced here as preset, incremental radial displacements. The computed fracture patterns and the order in which various cracks develop match what is seen in experiments. The model's robustness is tested under different stochastic realizations and discretization grid types.

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“…No significant differences on crack patterns were observed between models with = 1 and = 2. 43 In this work we use the model with = 1.…”

Section: Brief Review Of Peridynamic Theory For Elastic Brittle Matermentioning

confidence: 99%

A peridynamic model for damage and fracture in porous materials

Chen¹,

Niazi²,

Bobaru³

2019

Preprint

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(This paper is submitted to "International Journal of Rock Mechanics and Mining Sciences") We introduce a peridynamic (PD) model for simulating damage and fracture in porous materials based on an Intermediate Homogenization (IH) approach. In this approach, instead of explicitly representing the detailed pore geometry, we use homogenization but maintain some information about the microstructure (porosity) in the model. Porosity is introduced in the model as initial peridynamic damage, implemented by stochastically pre-breaking peridynamic bonds to match the desired porosity value. We validate the model for elastodynamics with wave propagation in porous glasses, where we match observed wave propagation speeds and the apparent elastic moduli for various porosities. The model is then used to study the fracture behavior of Berea sandstone under three-point bending loading conditions. We validate the model for fracture problems using the case of failure in a sandstone sample with an off-center pre-notch under three-point bending. The IH-PD results agree very well with experiments: we obtain different failure modes depending on the length of the off-center pre-notch. When the pre-notch is short, most damage (and the subsequent failure) happens in the center of the beam (largest tensile stresses in an un-notched sample). In this case, material porosity makes the fracture behavior “insensitive” to the presence of the off-center pre-notch. When the pre-notch is long, damage starts from near its tip, and progresses in mixed mode towards the loading point. The model captures the location of crack initiation to be the right-corner of the notch, exactly as shown by the experimental acoustic emission results. A fully-homogenized model for the porous sandstone fails to reproduce the failure mode sensitivity on the pre-notch length. The results show the importance of using the IH-PD model when trying to capture the important effects local heterogeneities (like pores) have on damage initiation and growth in porous materials.

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Elastic vortices and thermally-driven cracks in brittle materials with peridynamics

Cited by 72 publications

References 37 publications

Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods

A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete

A peridynamic model for damage and fracture in porous materials

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