The J-area integral applied in peridynamics

Stenström, Christer; Eriksson, Kjell

doi:10.1007/s10704-020-00505-8

Cited by 7 publications

(2 citation statements)

References 36 publications

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“…The SIF was calculated from the J-integral, using the finite element method by (Toribio et al, 2021;Christer;Kjell, 2021) extended a work to include the area integral (J) by deriving it as a function of displacements only, to also obtain the alternative method of calculating (J) in peri-dynamics. Therefore, the stress intensity factor at crack tip were calculated by the stress extrapolation method (Luo et al, 2021) such as the stress intensity factor (KI, KII) and the integral of the contour (J).…”

Section: Introductionmentioning

confidence: 99%

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Bentahar,

Youcef,

Mahmoudi

et al. 2024

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Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

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Section: Introductionmentioning

confidence: 99%

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Bentahar,

Youcef,

Mahmoudi

et al. 2024

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“…Le and Bobaru [15] investigated the performance of the different surface effect corrections in PD J-integral evaluation. Stenström and Eriksson developed the contour [21] and domain [22] forms of the PD J-integral based on the displacement field in BBPD. Those studies mentioned above only discussed mode-I fracture conditions.…”

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confidence: 99%

Static and dynamic mechanical behaviors of cracked Mindlin plates in ordinary state-based peridynamic framework

et al. 2022

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An ordinary state-based peridynamic (PD) model based on the Mindlin plate theory is pre sented to deal with fracture mechanics problems. Static and dynamic stress resultant intensity factors regarded as the primary fracture parameters for plate structures are evaluated by the displacement extrapolation method. Owing to the PD surface effect, however, the accuracy of the displacement field near crack surfaces is significantly affected. Therefore, the arbitrary horizon domain method is adopted to correct the surface effect. It derives the variable PD parameters to properly describe mechanical behaviors for each material point. Several numerical examples are investigated to examine the per formance of the presented method. It indicates that the PD Mindlin plate model incorporated with the arbitrary horizon domain method validly minimizes the influence from the PD surface effect and provides an effective approach to evaluate static and dynamic moment intensity factors. Keywords Peridynamics • Plate structures • Arbitrary horizon domain • PD surface effect • Moment intensity factors 1 IntroductionPeridynamics (PD) [1,2], which does not require spatial derivatives in its governing equations, has been developed to simulate different kinds of complicated fracture problems. For thin-walled struc tures, a shell model is an effective approach with less computation time than a 3D solid model. In the shell model, 2D plane stress and plate bending formulae are adopted to treat in-plane and out of-plane deformations, respectively. However, in contrast to 2D plane stress problems, the studies in plate bending problems are relatively few in the PD literature. O'Grady and Foster derived a non ordinary state-based peridynamic (NOSPD) model for Kirchhoff-Love plates [3] and shells [4] from the concept of rotational springs between interaction bonds. Diyaroglu et al.[5] developed a bond-based peridynamic (BBPD) model for beams and plates with transverse shear deformation. Chowdhury et al. [6] intro

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Mode-I J-integral via peridynamic stresses

2023

Int J Fract

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The J-area integral applied in peridynamics

Cited by 7 publications

References 36 publications

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Static and dynamic mechanical behaviors of cracked Mindlin plates in ordinary state-based peridynamic framework

Mode-I J-integral via peridynamic stresses

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