Peridynamic modelling of periodic microstructured materials

Xia, Wenxuan; Öterkuş, Erkan; Oterkus, Selda

doi:10.1016/j.prostr.2020.10.096

Cited by 11 publications

(3 citation statements)

References 25 publications

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“…However, if the variable porosity is concerned ( 16) with high ratios, direct modelling might be challenging. Second, the homogenization approach, in which the material is assumed to be homogeneous with reduced material modulus [34,35], can be employed for the regular microstructure cases. This technique, however, omits the random or complex micro-structure effects.…”

Section: Porosity Implementationmentioning

confidence: 99%

“…Oterkus et al [33] developed a coupled model for fluid driven fracture in porous media. Xia et al [34,35] proposed a homogenization scheme using a representative volume element approach for periodically micro-structured materials, e.g., composites, porous media so as to predict effective material properties from the PD displacement gradient tensor. Li et al [36] investigated the influence of porosity on the fracture behaviour of brittle granular materials.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics

Özdemir

Oterkus

Öterkuş

et al. 2021

Engineering with Computers

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Reliable evaluation of mechanical response in a porous solid might be challenging without any simplified assumptions. Peridynamics (PD) perform very well on a medium including pores owing to its definition, which is valid for entire domain regardless of any existed discontinuities. Accordingly, porosity is defined by randomly removing the PD interactions between the material points. As wave propagation in a solid body can be regarded as an indication of the material properties, wave propagation in porous media under an impact loading is studied first and average wave speeds are compared with the available reference results. A good agreement between the present and the reference results is achieved. Then, micro-cracks are introduced into porous media to investigate their influence on the elastic wave propagation. The micro-cracks are considered in both random and regular patterns by varying the number of cracks and their orientation. As the porosity ratio increases, it is observed that wave propagation speed drops considerably as expected. As for the cases with micro-cracks, the average wave speeds are not influenced significantly in random micro-crack configurations, while regular micro-cracks play a noticeable role in absorbing wave propagation depending on their orientation as well as the number of crack arrays in y-direction.

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Section: Porosity Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics

Özdemir

Oterkus

Öterkuş

et al. 2021

Engineering with Computers

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“…By considering the micromechanical model of a layered composite under uniaxial stress, Silling (2014) demon-strated that nonuniformity of the macroscopic strains leads to nonlocality in a homogenized model. The peridynamic counterpart of the computational homogenization direction is started by Madenci with coauthors [16,17,41,61] who proposed prediction of the effective properties for the peridynamic unit cell model subjected to the classical periodical boundary conditions. The most important specification of computational homogenization is an introduction of the periodical boundary conditions at the unit cell.…”

Section: Introductionmentioning

confidence: 99%

Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Buryachenko¹

2022

Preprint

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In contrast to the classical local theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48:175-–209) is free of any spatial derivatives of the displacement field. A thermoelastic composite materials (CMs) theory with nonlocal peridynamic properties of multiphase constituents of arbitrary geometry is analyzed for periodic structure CMs subjected to the volumetric periodic boundary conditions. Effective properties of peridynamic CM are expressed through the introduced micropolarization tensor averaged over the extended inclusion phase. Decompositions of material and field parameters are performed to analyze the fields produced by both mechanical and eigenfield loading. Transformation field analysis (TFA) and clustering discretization method (defining offline linear stage) adapted to the linear peridynamic micromechanics are proposed by the use of formal similarity of proposed methods with corresponding approaches of local micromechanics. Stress and displacement in each cluster are assumed to be constant and linear functions, respectively, even when a cluster is not a simply connected area in general. This fact greatly reduces the degree of freedom in the problem being considered. The clustering version of TFA for the homogenization of nonlinear peridynamics micromechanics is based on employing eigenstrains to account for inelastic displacements arising from material nonlinearity. The scheme of numerical solution of linear thermoelastic peridynamic problem and estimation of influence functions are presented.

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Computational Homogenization in Linear Peridynamic Micromechanics of Periodic Structure CMs

Buryachenko¹

2012

Local and Nonlocal Micromechanics of Heterogeneous Materials

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Peridynamic modelling of periodic microstructured materials

Cited by 11 publications

References 25 publications

Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics

Evaluation of dynamic behaviour of porous media including micro-cracks by ordinary state-based peridynamics

Transformation field analysis and clustering discretization method in pyridynamic micromechanics of composites

Computational Homogenization in Linear Peridynamic Micromechanics of Periodic Structure CMs

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