Non-ordinary state-based peridynamic analysis of stationary crack problems

Breitenfeld, Michael; Geubelle, Philippe H.; Weckner, Olaf; Silling, Stewart A.

doi:10.1016/j.cma.2014.01.002

Cited by 296 publications

(137 citation statements)

References 28 publications

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“…The capability of peridynamics in 3D problems has been successfully illustrated in numerous studies [19,31]. Therefore, it is possible to extend the proposed fiber modeling approach to 3D problems.…”

Section: Future Workmentioning

confidence: 98%

“…For a linearly elastic material, Breitenfeld et al [31] developed a numerical discretization scheme to solve the peridynamic equilibrium equations (Eq. (6)).…”

Section: Proposed Non-ordinary State-based Peridynamic Formulationmentioning

confidence: 99%

“…Additional analysis methods had been introduced to generalize the peridynamic formulation: (1) The ordinary state based peridynamics (OSBPD) generalizes the bond-based peridynamics to include any Poissons ratio by defining central force states of unequal magnitudes [24,30]; and (2) in the non-ordinary state based peridynamic (NOSBPD) method, non-parallel and unequal force states are used to model interactions between material points [24,26,31]. Therefore, the NOSBPD method can be applied to material models with any Poissons ratio.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Meshless modeling framework for fiber reinforced concrete structures

Yaghoobi

Chorzepa

2015

Computers & Structures

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Section: Future Workmentioning

confidence: 98%

“…For a linearly elastic material, Breitenfeld et al [31] developed a numerical discretization scheme to solve the peridynamic equilibrium equations (Eq. (6)).…”

Section: Proposed Non-ordinary State-based Peridynamic Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Meshless modeling framework for fiber reinforced concrete structures

Yaghoobi

Chorzepa

2015

Computers & Structures

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“…The response of a bond is independent of the other bonds in the bond-based peridynamic formulation, which makes it limited to the constitutive models with a fixed Poisson's ratio [5,28]. To eliminate the limitations including the limited Poisson's ratio, a reformulation of the bond-based PD relation, called the state-based peridynamic model, was proposed by Silling and coworkers [29][30][31], and it has been employed to describe the mechanical and fracture behavior of more general materials [32,33].…”

Section: Introductionmentioning

confidence: 99%

An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis

Huang

Qiao

2015

International Journal of Mechanical Sciences

219

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“…Since then, peridynamics has been successfully utilized to analyze various problems including progressive failure [11,12], phase transformation [13], and stationary and dynamic fracture [14][15][16] at both macro-and microscales, and it shows great potential analogous but advantageous to both classical meshfree and molecular dynamic methods.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Peridynamic Modeling and Simulation on Crack Propagation in Concrete Structures

Huang

Liu

2015

Mathematical Problems in Engineering

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An extended peridynamic approach for crack propagation analysis in concrete structures was proposed. In the peridynamic constitutive model, concrete material was described as a series of interacting particles, and the short-range repulsive force and anisotropic behavior of concrete were taken into account in the expression of the interactive bonding force, which was given in terms of classical elastic constants and peridynamic horizon. The damage of material was defined locally at the level of pairwise bond, and the critical stretch of material bond was described as a function of fracture strength in the classical concrete failure theory. The efficiency and accuracy of the proposed model and algorithms were validated by simulating the propagation of mode I and I-II mixed mode cracks in concrete slabs. Furthermore, crack propagation in a double-edge notched concrete beam subjected to four-point load was simulated, in which the experimental observations are captured naturally as a consequence of the solution.

show abstract

Non-ordinary state-based peridynamic analysis of stationary crack problems

Cited by 296 publications

References 28 publications

Meshless modeling framework for fiber reinforced concrete structures

Meshless modeling framework for fiber reinforced concrete structures

An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis

Nonlocal Peridynamic Modeling and Simulation on Crack Propagation in Concrete Structures

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