Dynamic fracture analysis of functionally graded materials using ordinary state-based peridynamics

Özdemir, Murat; Kefal, Adnan; Imachi, Misako; Tanaka, Satoyuki; Öterkuş, Erkan

doi:10.1016/j.compstruct.2020.112296

Cited by 53 publications

(31 citation statements)

References 37 publications

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“…Another approach that can be used is to assign the inertia term given in Eq. (19) to 0 and perform implicit solution by solving a matrix system. Again, such system may require large memory and special solution techniques to obtain the solution.…”

Section: Static Problemsmentioning

confidence: 99%

Determination of horizon size in state-based peridynamics

Wang

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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Peridynamics is based on integro-differential equations and has a length scale parameter called horizon which gives peridynamics a non-local character. Currently, there are three main peridynamic formulations available in the literature including bond-based peridynamics, ordinary state-based peridynamics and non-ordinary state-based peridynamics. In this study, the optimum horizon size is determined for ordinary state-based peridynamics and non-ordinary state-based peridynamics formulations by using uniform and non-uniform discretisation under dynamic and static conditions. It is shown that the horizon sizes selected as optimum sizes for uniform discretisation can also be used for non-uniform discretisation without introducing significant error to the system. Moreover, a smaller horizon size can be selected for non-ordinary state-based formulation which can yield significant computational advantage. It is also shown that same horizon size can be used for both static and dynamic problems. Keywords Peridynamics • Horizon • State-based • Ordinary state-based • Non-ordinary state-based 1 Introduction Solid mechanics is an important area of engineering dealing with deformations of materials and structures under external loading conditions. Continuum mechanics has been widely used for this purpose for the last two hundred years, and there are currently different continuum mechanics formulations available in the literature with different advantages and limitations. The most common continuum mechanics formulation was developed by Cauchy, and the equation of motion of the fundamental object of continuum mechanics, i.e. "material point", is expressed in the form of a partial differential equation. Since the analytical solution of this equation is limited to particular geometries, boundary conditions and material systems, different numerical techniques including finite element method have been developed to obtain solution for numerous problems of interest. However, due to the spatial derivatives in the partial differential equations, the standard solution procedures become invalid if discontinuities such as cracks exist in the solution domain. In such cases, additional steps should be taken to get around the discontinuity problem. As an alternative approach, Silling [1] developed a new continuum mechanics formulation and named it as "peridynamics". There are several fundamental differences between peridynamics and Cauchy's continuum mechanics (CCM) formulation. First of all, the equation of motion of a material point in peridynamics is in integral form and does not contain any spatial derivatives. Therefore, it does not suffer from the discontinuity problem mentioned earlier. Moreover, peridynamics [2-20] is a non-local continuum mechanics formulation Communicated by Luca Placidi.

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Section: Static Problemsmentioning

confidence: 99%

Determination of horizon size in state-based peridynamics

Wang

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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“…This issue has been addressed mainly in the context of modeling functionally graded materials using PD. The most common procedure is to average the parameters of the constituent materials [60][61][62]. More elaborate concepts contain weighting parameters following different approaches of weighting.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

2021

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Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.

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“…Moreover, PD is a non-local continuum mechanics formulation and it has a length-scale parameter, horizon, which defines range of non-local interactions between material points. PD has been used for analysing different types of materials including metals and composites [7–10] and is suitable for multiphysics analysis [11–15]. Moreover, several peridynamic formulations are available in the literature to analyse beams, plates and shells [16–21].…”

Section: Introductionmentioning

confidence: 99%

A state-based peridynamic formulation for functionally graded Kirchhoff plates

Yang

Öterkuş

Oterkus

2020

Mathematics and Mechanics of Solids

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Functionally graded materials are a potential alternative to traditional fibre-reinforced composite materials as they have continuously varying material properties which do not cause stress concentrations. In this study, a state-based peridynamic model is presented for functionally graded Kirchhoff plates. Equations of motion of the new formulation are obtained using the Euler–Lagrange equation and Taylor’s expansion. The formulation is verified by considering several benchmark problems including a clamped plate subjected to transverse loading and a simply supported plate subjected to transverse loading and inclined loading. The material properties are chosen such that Young’s modulus is assumed to be varied linearly through the thickness direction and Poisson’s ratio is constant. Peridynamic results are compared against finite element analysis results, and a very good agreement is obtained between the two approaches.

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Dynamic fracture analysis of functionally graded materials using ordinary state-based peridynamics

Cited by 53 publications

References 37 publications

Determination of horizon size in state-based peridynamics

Determination of horizon size in state-based peridynamics

Nonlocal wrinkling instabilities in bilayered systems using peridynamics

A state-based peridynamic formulation for functionally graded Kirchhoff plates

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