Numerical modelling of rock materials with polygonal finite elements

This article presents some preliminary results on numerical modeling of rock ma-terials with polygonal ﬁnite elements. A method to describe the rock microstructure based onVoronoi diagrams, representing the rock grain texture, is sketched. In this method, the mineralsconstituting the rock are represented as Voronoi cells which themselves are polygonal ﬁnite ele-ments. A three-point bending problem under plane stress linear elasticity condition is solved inorder to compare the performance of polygonal elements to ordinary ﬁnite elements. Moreover,it is demonstrated by solving the stress state in uni-axial compression that the heterogeneitydescribed with the present method results in short-range tensile stresses which could initiatemode-I cracks.

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Numerical modeling of thermo‐mechanical failure processes in granitic rock with polygonal finite elements

International Journal for Numerical and Analytical Methods in Geomechanics ◽

10.1002/nag.3247 ◽

2021 ◽

Author(s):

Timo Saksala

Keyword(s):

Numerical Modeling ◽

Finite Elements ◽

Granitic Rock ◽

Mechanical Failure ◽

Polygonal Finite Elements

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Numerical modeling of two-phase binary fluid mixing using mixed finite elements

Computational Geosciences ◽

10.1007/s10596-012-9306-2 ◽

2012 ◽

Vol 16 (4) ◽

pp. 1101-1124 ◽

Cited By ~ 9

Author(s):

Shuyu Sun ◽

Abbas Firoozabadi ◽

Jisheng Kou

Keyword(s):

Numerical Modeling ◽

Finite Elements ◽

Mixed Finite Elements ◽

Fluid Mixing ◽

Two Phase ◽

Binary Fluid

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Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

European Journal of Computational Mechanics ◽

10.1080/17797179.2012.702432 ◽

2012 ◽

Vol 21 (1-2) ◽

pp. 92-102 ◽

Cited By ~ 2

Author(s):

Kaliappan Jayabal ◽

Andreas Menzel

Keyword(s):

Finite Elements ◽

Three Dimensional ◽

Voronoi Cell ◽

Polygonal Finite Elements

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A Study Regarding the Unsteady Heat Transfer and Phase Change

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.659.353 ◽

2014 ◽

Vol 659 ◽

pp. 353-358

Author(s):

Gelu Coman ◽

Cristian Iosifescu ◽

Valeriu Damian

Keyword(s):

Heat Transfer ◽

Numerical Modeling ◽

Temperature Field ◽

Temperature Distribution ◽

Finite Elements ◽

Experimental Research ◽

Theoretical Study ◽

Ice Formation ◽

Unsteady Heat Transfer ◽

Cooling Pipes

The paper presents the experimental and theoretical study for temperature distribution around the cooling pipes of an ice rink pad. The heat transfer in the skating rink track is nonstationary and phase changing. In case of skating rinks equipped with pipe registers, the temperature field during the ice formation process can’t be modeled by analytical methods. The experimental research was targeted on finding the temperatures in several points of the pad and also details on ice shape and quality around the pipes. The temperatures measured on the skating ring surface using thermocouples is impossible due to the larger diameter of the thermocouple bulb compared with the air-water surfaces thickness. For this reason we used to measure the temperature by thermography method, thus reducing the errors The experimental results were compared against the numerical modeling using finite elements.

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Polygonal finite elements for three-dimensional Voronoi-cell-based discretisations

European Journal of Computational Mechanics ◽

10.13052/17797179.2012.702432 ◽

2012 ◽

Author(s):

Kaliappan Jayabal ◽

Andreas Menzel

Keyword(s):

Finite Element ◽

Finite Elements ◽

Three Dimensional ◽

Specific Property ◽

Voronoi Cell ◽

Polycrystalline Materials ◽

Element Formulation ◽

Hybrid Finite Element ◽

Grain Structures ◽

Polygonal Elements

Hybrid finite element formulations in combination with Voronoi-cell-based discretisation methods can efficiently be used to model the behaviour of polycrystalline materials. Randomly generated three-dimensional Voronoi polygonal elements with varying numbers of surfaces and corners in general better approximate the geometry of polycrystalline microor rather grain-structures than the standard tetrahedral and hexahedral finite elements. In this work, the application of a polygonal finite element formulation to three-dimensional elastomechanical problems is elaborated with special emphasis on the numerical implementation of the method and the construction of the element stiffness matrix. A specific property of Voronoi-based discretisations in combination with a hybrid finite element approach is investigated. The applicability of the framework established is demonstrated by means of representative numerical examples.

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