Dynamic Crack Propagation and Its Interaction With Micro-Cracks in an Impact Problem

Candaş, Adem; Öterkuş, Erkan; Irmak, Cevat Erdem

doi:10.1115/1.4047746

Cited by 30 publications

(16 citation statements)

References 59 publications

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“…The presence of the second-order time derivative of the solution u in (67) means in addition to the boundary constraints (68), (69), initial conditions also need to be specified. The initial condition involves prescribing the initial values of the solution and its first derivative.…”

Section: Constitutive Modelmentioning

confidence: 99%

“…Peridynamics is a reformulation of the classical elasticity theory with extended capabilities of modelling discontinuous system response and long-range force interaction. Since its introduction, theory continues to receive growing interest from researchers and have thus found application in solving a wide range of engineering problems [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70]. This is because it offers a theoretical and mathematical framework that allow for the modelling of systems with singularities without the need for modification of the governing equations.…”

Section: Introductionmentioning

confidence: 99%

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A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

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Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.

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Section: Constitutive Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A computational homogenization framework for non-ordinary state-based peridynamics

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

Self Cite

View full text Add to dashboard Cite

show abstract

“…Peridynamics has been successfully applied in studying a wide spectrum of physical phenomena in the realm of solid and fluid mechanics. These include studies in dynamic crack propagation [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], fatigue analysis [36][37][38][39][40], vibration and wave dispersion [41][42][43][44][45][46]. In the field of heat transport, considerable research efforts have been expended in developing and applying peridynamic framework to model heat transport phenomena.…”

Section: Introductionmentioning

confidence: 99%

Static condensation of peridynamic heat conduction model

Galadima

Öterkuş

Oterkus

2022

Mathematics and Mechanics of Solids

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A model order reduction methodology for reducing the order of the peridynamic transient heat model is proposed. This methodology is based on the static condensation procedure. To set the development of the model reduction procedure on a sound mathematical setting, a nonlocal vector calculus was employed in the formulation of the heat transport problem. The model order reduction framework proposed in this study provides a technique to reduce the dimensionality of a peridynamic transport model while still maintaining accurate prediction of the model response. Moreover, the methodology can be adaptively applied to accommodate different resolution requirements for different sections of the model. Using numerical experiments, the proposed methodology is shown to be capable of accurately reproducing results of the full peridynamic transient heat transport problem.

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“…This allows the analysis of evolving discontinuities such as cracks in a natural way. Recent numerical studies illustrate the ability of peridynamics to capture complex fracture phenomena such as crack initiation [11,14,20], crack branching [7], crack kinking [5] and crack interaction with initial heterogeneities, such as holes and pores [1,2,16,27].…”

Section: Introductionmentioning

confidence: 99%

Beam buckling analysis in peridynamic framework

et al. 2022

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Peridynamics is a non-local continuum theory which accounts for long-range internal force/moment interactions. Peridynamic equations of motion are integro-differential equations, and only few analytical solutions to these equations are available. The aim of this paper is to formulate governing equations for buckling of beams and to derive analytical solutions for critical buckling loads based on the nonlinear peridynamic beam theory. For three types of boundary conditions, explicit expressions for the buckling loads are presented. The results are compared with the classical results for buckling loads. A very good agreement between the non-local and the classical theories is observed for the case of the small horizon sizes which shows the capability of the current approach. The results show that with an increase of the horizon size the critical buckling load slightly decreases for the fixed overall stiffness of the beam.

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Dynamic Crack Propagation and Its Interaction With Micro-Cracks in an Impact Problem

Cited by 30 publications

References 59 publications

A computational homogenization framework for non-ordinary state-based peridynamics

A computational homogenization framework for non-ordinary state-based peridynamics

Static condensation of peridynamic heat conduction model

Beam buckling analysis in peridynamic framework

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