Peridynamic Functionally Graded and Porous Materials: Modeling Fracture and Damage

Chen, Ziguang; Niazi, Sina; Zhang, Guanfeng; Bobaru, Florin

doi:10.1007/978-3-319-22977-5_36-1

Cited by 14 publications

(30 citation statements)

References 47 publications

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“…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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“…In this section, we briefly discuss two types of homogenization of peridynamic models for transversely loaded FRCs: the fully homogenized (FH-PD) model and intermediately homogenized (IH-PD) model. These models have been previously evaluated for wave propagation and dynamic and quasi-static fracture in functionally graded and porous materials [32]. Thus, the transverse Young's modulus we will match with our FH-PD model is:…”

Section: Reinforced Compositesmentioning

confidence: 99%

“…is a parameter that accounts for the packing and fiber geometry ( = 2 for fibers with square or round cross-section) [25,32,35]. Here, we consider the harmonic averaging method as follows:…”

Section: The Fully Homogenized Peridynamic Modelmentioning

confidence: 99%

“…7.b. We perform a δ-convergence study for the elastic behavior in bending of the sample with the notch (see [32]). To simulate the three-point bending test using the IH-PD model, and perform theconvergence study (in terms of the horizon size while keeping the number of nodes covered by a node's horizon roughly the same), we create non-uniform meshes (since these conform better to the round notch tip) with three different element sizes of 75, 56, and 37.5 μm (corresponding to horizon sizes of 300, 225, and 150 μm respectively) (see Fig.…”

Section: Case Of the Composite With A Large Elasticity Contrast Bementioning

confidence: 99%

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A Stochastic Homogenized Peridynamic Model for Intraply Fracture in Fiber-Reinforced Composites

Mehrmashhadi¹,

Chen²,

Zhao³

et al. 2019

Preprint

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The quasi-static transverse fracture behavior in unidirectional fiber-reinforced composites (FRCs) is investigated using a new intermediately-homogenized peridynamic (IH-PD) model and a fully homogenized peridynamic (FH-PD) model. The novelty in the IH-PD model here is accounting for the topology of the fiber-phase in the transverse sample loading via a calibration to the Halpin-Tsai model. Both models can capture well the measured load-displacement behavior observed experimentally for intraply fracture, without the need for an explicit representation of microstructure geometry of the FRC. The IH-PD model, however, is more accurate and produces crack path tortuosity as well as a non-monotonic load-crack-opening softening curve, similar to what is observed experimentally. These benefits come from the preservation of some micro-scale heterogeneity, stochastically generated in the IH-PD model to match the composite’s fiber volume fraction, while its computational cost is equivalent to that of an FH-PD model. We also present a three-point bending transverse loading case in which the two models lead to dramatically different failure modes: the FH-PD model shows that failure always starts from the off-center pre-notch, while the IH-PD model, when the pre-notch is sufficiently off-center, finds that the composite fails from the center of the sample, not from the pre-notch. Experiments that can confirm these findings are sought.

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“…We perform a δ-convergence study (horizon size decreases while keeping the number of nodes covered by a node's horizon roughly the same, see [28]) on the monolithic PMMA to see if the fracture patterns and crack speed converge. We use horizon sizes of 3.2, 1.6, and 0.8 mm with the horizon factor (the ratio of horizon size over the discretization size) of four.…”

Section: Convergence Study For Dynamic Fracture Pmmamentioning

confidence: 99%

Uncovering the dynamic fracture behavior of PMMA

Mehrmashhadi¹,

Wang²,

Bobaru³

2019

Preprint

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Experimental investigations of dynamic crack propagation in PMMA induced by impact show single cracks running at around 300-400 m/s. Existing numerical models for simulating dynamic fracture in PMMA consistently produce crack propagation speeds significantly higher than those measured experimentally. Here we uncover the reason for this puzzle by showing that localized softening in the fracture process zone (caused by heating due to high strain rates in front of the crack tip), leads to crack propagation speeds that match the observed ones. We introduce a new constitutive model in our peridynamic formulation for PMMA to account for material softening in the crack tip region. With the new model, the computed crack speed and crack length evolution match very closely those found experimentally.

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Peridynamic Functionally Graded and Porous Materials: Modeling Fracture and Damage

Cited by 14 publications

References 47 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 Homogenized Peridynamic Model for Intraply Fracture in Fiber-Reinforced Composites

Uncovering the dynamic fracture behavior of PMMA

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