An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory

Kilic, Bahattin; Madenci, Erdogan

doi:10.1016/j.tafmec.2010.08.001

Cited by 388 publications

(166 citation statements)

References 19 publications

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“…Several scientists tried to use anatomical features as input parameters in statistical explanations. For example, the occurrence of ray cells (Barkas 1941;Boutelje 1962;Kelsey 1963;Keller and Thiercelin 1975;Guitard and El Amri 1987) and the shape of cells (Mariaux and Narboni 1978;Masseran and Mariaux 1985) were tested as possible explanations of shrinkage variability. In 1989, Mariaux observed that the transverse anisotropy of tissues depends on the mean elongation of the cell, but that shrinkage was not isotropic for "isotropic" cells (same mean diameter in both the radial and tangential directions).…”

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confidence: 99%

New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods

Perré

Almeida

Ayouz

et al. 2016

Annals of Forest Science

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Key message The real tissue structure, including local anisotropy directions, is defined from anatomical images of wood. Using this digital representation, thermal/mass diffusivity and mechanical properties (stiffness, large deformation, rupture) are successfully predicted for any anatomical pattern using suitable meshless methods. Introduction Wood, an engineering material of biological origin, presents a huge variability among and within species. Understanding structure/property relationships in wood would allow engineers to control and benefit from this variability. Several decades of studies in this domain have emphasised the need to account simultaneously for the phase properties and the phase morphology in order to be able to predict wood properties from its anatomical features. This work is focused on the possibilities offered by meshless computational methods to perform upscaling in wood using actual tissue morphologies obtained by microscopic images. Methods After a section devoted to the representation step, the digital representation of wood anatomy by image processing and grid generation, the papers focuses on three meshless methods applied to predict different macroscopic properties in the transverse plane of wood (spruce earlywood, spruce latewood and poplar): Lattice Boltzmann Method (LBM) allows thermal conductivity and mass diffusivity to be predicted, Material Point Method (MPM) deals with rigidity and compression at large deformations and peridynamic method is used to predict the fracture pathway in the cellular arrangement. Results This work proves that the macroscopic properties can be predicted with quite good accuracy using only the cellular structure and published data regarding the cell wall properties. A whole set of results is presented and commented, including the anisotropic ratios between radial and tangential directions.

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confidence: 99%

New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods

Perré

Almeida

Ayouz

et al. 2016

Annals of Forest Science

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“…In order to apply the peridynamic equations of motion to solve quasi-static problems, Kilic and Madenci [7] introducing an artificial damping to guide the solution to approach the steady state and using the Adaptive Dynamic Relaxation (ADR) scheme proposed by Underwood [8] to determine the most effective damping coefficient at each time step n, as follows:…”

Section: Discretization and Numerical Implementationmentioning

confidence: 99%

Peridynamic Modeling of plain concrete structures under monotonic loading

Lu¹,

Zhang²,

Chen³

2017

Proceedings of the Second International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2017)

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“…Kilic and Madenci [45] effectively used the adaptive dynamic relaxation method [46] for obtaining steady-state solutions of bond based peridynamic equations. In this study, the dynamic relaxation (DR) method is adopted to obtain quasi-static solutions of the NOSBPD equilibrium equation, (Eq.…”

Section: Appendix B Dynamic Relaxationmentioning

confidence: 99%

“…Yaghoobi, M.G. Chorzepa / Computers and Structures 161 (2015)[43][44][45][46][47][48][49][50][51][52][53][54] …”

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confidence: 99%

Meshless modeling framework for fiber reinforced concrete structures

Yaghoobi

Chorzepa

2015

Computers & Structures

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An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory

Cited by 388 publications

References 19 publications

New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods

New modelling approaches to predict wood properties from its cellular structure: image-based representation and meshless methods

Peridynamic Modeling of plain concrete structures under monotonic loading

Meshless modeling framework for fiber reinforced concrete structures

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