Редактирование: V-model
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[[Файл: Fig1 compos.png|450px|thumb|right| SEM image of composite consisting | [[Файл: Fig1 compos.png|450px|thumb|right| SEM image of composite consisting | ||
of nanoparticles bonded by a copolymer. (N. Preda, et. al., Mater. Res. Bull. | of nanoparticles bonded by a copolymer. (N. Preda, et. al., Mater. Res. Bull. | ||
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== Introduction == | == Introduction == | ||
− | The article is based on the | + | The article is based on the paper '''V.A. Kuzkin and I.E. Asonov "[http://pre.aps.org/abstract/PRE/v86/i5/e051301 Vector-based model of elastic bonds for simulation of granullar solids]"// Phys. Rev. E, 86, 051301, 2012'''. Author's copy can be downloaded [[Медиа: Kuzkin_2012_PRE_proof2.pdf |'''here''']]. |
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The vectors are used for description of different types of bond's deformation. The expression for potential energy corresponding to tension/compression, shear, bending, and torsion of the bond is proposed. Forces and torques acting between particles are derived from the potential energy. | The vectors are used for description of different types of bond's deformation. The expression for potential energy corresponding to tension/compression, shear, bending, and torsion of the bond is proposed. Forces and torques acting between particles are derived from the potential energy. | ||
Two approaches for calibration of V-model parameters for bonds with different length/thickness ratios are presented. Simple analytical formulas connecting geometrical and elastic characteristics of the bond with parameters of the V-model are derived. Main aspects of numerical implementation of the model are discussed. | Two approaches for calibration of V-model parameters for bonds with different length/thickness ratios are presented. Simple analytical formulas connecting geometrical and elastic characteristics of the bond with parameters of the V-model are derived. Main aspects of numerical implementation of the model are discussed. | ||
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== Advantages of the V-model == | == Advantages of the V-model == | ||
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* bonds can connect points inside the particles or lying on particles surfaces (not only particle centers) | * bonds can connect points inside the particles or lying on particles surfaces (not only particle centers) | ||
* fracture criterion for the bond can be used if required | * fracture criterion for the bond can be used if required | ||
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== Debugging == | == Debugging == | ||
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* '''Pure torsion'''. Positions of both particles are fixed. Orientation of one particle is fixed. Another particle is rotating around the bond. The torque acting on the particles is calculated. | * '''Pure torsion'''. Positions of both particles are fixed. Orientation of one particle is fixed. Another particle is rotating around the bond. The torque acting on the particles is calculated. | ||
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+ | == Some examples == | ||
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+ | {|align="right" | ||
+ | |-valign="top" | ||
+ | |[[Файл:Rod instability.jpg|150px|thumb|right| Rod under the action of following shear force, acting on the rod's end]] | ||
+ | |[[Файл:Plate instability.jpg|150px|thumb|right| Plate under the action of following compressive forces, acting along the edge of the plate]] | ||
+ | |[[Файл:3D rod torsion.jpg|150px|thumb|right| Torsion of 3D rod-like body]] | ||
+ | |} | ||
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+ | Press the links below to see animated gifs: | ||
+ | * [[Media: Buckling_rod_following_force.gif | Buckling of the discrete rod under the action of following force]] | ||
+ | * [[Media: Instability under torsion.gif | Instability of a discrete rod under torsion ]] | ||
+ | * [[Media: Nikolai paradox.gif | Rod under the action of following torque (Nikolai paradox)]] | ||
+ | * [[Media: wire_torsion.gif | Torsion of the wire]] | ||
+ | * [[Media:Buckling_discrete_shell_light.gif | Buckling of the discrete hemisphere]] | ||
+ | * [[Media: Shell_between_walls.gif | Discrete spherical shell bouncing between rigid walls]] | ||
+ | * [[Media: Shell impact.gif | Discrete spherical shell impacting rigid walls]] | ||
== DEM packages using the V-model == | == DEM packages using the V-model == | ||
* [http://www.liggghts.com/ '''LIGGGHTS'''], details of implementation and some examples are given [[Implementation_of_V_model_in_LIGGGHTS | here]]. | * [http://www.liggghts.com/ '''LIGGGHTS'''], details of implementation and some examples are given [[Implementation_of_V_model_in_LIGGGHTS | here]]. | ||
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== History and acknowledgements == | == History and acknowledgements == | ||
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* [[Vitaly Kuzkin]] | * [[Vitaly Kuzkin]] | ||
* [[Игорь Асонов | Igor Asonov]] | * [[Игорь Асонов | Igor Asonov]] | ||
− | * [[ | + | * [[Виталий Кузькин: Избранные публикации | Selected publications of Vitaly Kuzkin]] |
[[Category: Потенциальные взаимодействия]] | [[Category: Потенциальные взаимодействия]] | ||
[[Category: Механика дискретных сред]] | [[Category: Механика дискретных сред]] |