A peridynamic approach for modeling of two dimensional functionally graded plates

Dördüncü, Mehmet; OLMUŞ, İbrahim; Rabczuk, Timon

doi:10.1016/j.compstruct.2021.114743

Cited by 24 publications

(6 citation statements)

References 57 publications

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“…[37] ve Dorduncu vd. [38] tarafından yapılan çalışmalarda detaylı olarak anlatılmıştır. FK malzemeler yapı içerisinde katmanları arasında sürekli geçişler sağlamaktadır ve her bir katmanı izotrop olarak farklı malzeme özelliği sergilemektedir.…”

Section: Sıradan Durum Bazlı Peridinamik Teorisiunclassified

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Investigation of fracture behaviour of one-dimensional functionally graded plates by using peridynamic theory

KAYA>

OLMUŞ

Dördüncü

2022

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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Composite materials are widely used in aerospace, military, and nuclear engineering fields due to their desirable properties such as lightness and high strength. The mismatch of the stiffness at the interfaces between distinct materials results in a stress concentration; thus, crack nucleation and inter-layer separations can be observed. The concept of functionally graded materials (FGMs) aims to achieve a structure whose material properties continuously vary in one or more coordinate directions. This continuous variation is obtained for the material properties of the FG structure.This situation provides a way to minimize the stress concentrations which may occur at the interfaces between the two different materials. FGMs are one of the most important structures in defense and aerospace industries owing to their superior properties. In order to design FG structures safely, it is very crucial to understand and investigate possible damages under different loads to increase the reliability of these structures. Since structural testing and analysis techniques may be costly, there is a necessity to use improved and accurate computational tools to predict the deformation and stress fields of the FG structures. Numerical modeling of the fracture and damage in FGMs remains a formidable challenge in computational mechanics due to the non-symmetric material variations in the FGMs. In PeriDynamic (PD) theory, the equations of classical continuum mechanics (CCM) are reformulated by replacing the derivatives with volumetric integral expressions. Hence, the equilibrium equations of PD theory are still valid even if the material includes a discontinuity, unlike CCM. In this study, the influence of the material variations in the FG plates on the crack nucleation and propagation is investigated by means of PD theory. As a result of the analysis, it is observed that the material distributions have an evident effect on the fracture behaviour of the plate, and the plate strength can be increased by tailoring the material properties in the FG plates.

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Section: Sıradan Durum Bazlı Peridinamik Teorisiunclassified

“…Dorduncu vd. [38] tarafından sunulan çalışmada ise bir yönlü ve iki yönlü FKM'lerin kırılma davranışı SBD PD teorisi kullanılarak incelenmiştir.…”

Section: Giriş (Introduction)unclassified

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Investigation of fracture behaviour of one-dimensional functionally graded plates by using peridynamic theory

KAYA>

OLMUŞ

Dördüncü

2022

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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“…Kefal et al [17] demonstrated how to use peridynamics for topology optimisation of cracked structures. There have also been many studies presenting peridynamic formulations for beams and plates to model isotropic materials [18–22], functionally graded materials [23–28], and composite materials [29,30]. Peridynamics has also been extended to model other physical fields.…”

Section: Introductionmentioning

confidence: 99%

Double horizon peridynamics

Yang

Öterkuş

Oterkus

et al. 2023

Mathematics and Mechanics of Solids

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In this study, a new double horizon peridynamics formulation was introduced by utilising two horizons instead of one as in traditional peridynamics. The new approach allows utilisation of large horizon sizes by controlling the size of the inner horizon size. To demonstrate the capability of the current approach, four different numerical cases were examined by considering static and dynamic conditions, different boundary and initial conditions, and different outer and inner horizon size values. For both static and dynamic cases, it was observed that as the inner horizon decreases, peridynamic solutions converge to classical continuum mechanics solutions even by using a larger horizon size value. Therefore, the proposed approach can serve as an alternative approach to improve computational efficiency of peridynamic simulations by obtaining accurate results with larger horizon sizes.

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“…Various PD models have been proposed over the years, such as bond-based peridynamic (BB-PD) models, state-based peridynamic (SB-PD) models, hybrid models leveraging PD and CCM, and analytical PD solutions. These PD models have been used successfully to tackle a variety of multi-physical issues, such as heat conduction (Bobaru and Duangpanya, 2010;Oterkus et al, 2014), fluid transport (Katiyar et al, 2014;Gao and Oterkus, 2019;Katiyar et al, 2020), material corrosion (Chen and Bobaru, 2015;De Meo et al, 2016;Jafarzadeh et al, 2018), etc., and PD also has been expanded in a variety of directions, such as dual-horizon PD (Ren et al, 2016(Ren et al, , 2017Rabczuk and Zhuang, 2021), PD plate/shell theory (Chowdhury et al, 2016;Zhang et al, 2021;Dorduncu et al, 2021), phase field based PD damage model (Roy et al, 2017(Roy et al, , 2021, wave dispersion analysis in PD (Gu et al, 2016;Butt et al, 2017;Zhang et al, 2019), weak form of PD (Madenci et al, 2018), PD least squares minimisation (Madenci et al, 2019b,a), coupling of FEM and ordinary state-based (OSB)/non-ordinary state-based (NOSB) PD (Yaghoobi and Chorzepa, 2018;Ni et al, 2021;Jin et al, 2021;Liu et al, 2021), higher-order PD (Yang et al, 2021a(Yang et al, , 2021b(Yang et al, , 2021c, etc. In comparison to the local theory, the non-local theory not only has a superior numerical well-posedness, but it also resembles the real physical process better due to its inherent length scale.…”

Section: Introductionmentioning

confidence: 99%

Explicit implementation of the non-local operator method: a non-local dynamic formulation for elasticity solid

Zhang¹

2022

IJHM

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This paper presents an explicit non-local operator method (NOM) for the dynamic analysis of elasticity solid problems. The NOM is based on so-called dual-supports, non-local operators and an operate energy functional ensuring stability. The non-local operators are the generalisation of the conventional differential operators. Combined with the variational principle, the non-local governing equations and non-local operator energy functional for linear elasticity solid are derived. The non-local governing equations and non-local operator energy functional are expressed as the integral forms of support and dual-support. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The NOM does not necessitate the use of any shape functions which may be complicated to construct and drastically facilitate the implementation. Several numerical examples are provided to highlight the method's capabilities.

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A peridynamic approach for modeling of two dimensional functionally graded plates

Cited by 24 publications

References 57 publications

Investigation of fracture behaviour of one-dimensional functionally graded plates by using peridynamic theory

Investigation of fracture behaviour of one-dimensional functionally graded plates by using peridynamic theory

Double horizon peridynamics

Explicit implementation of the non-local operator method: a non-local dynamic formulation for elasticity solid

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