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Journal articles on the topic 'Finite element and discrete element modelling'

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Published: 27 July 2024

Last updated: 29 July 2024

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1

Chen, Xudong, and Hongfan Wang. "Slope Failure of Noncohesive Media Modelled with the Combined Finite–Discrete Element Method." Applied Sciences 9, no. 3 (February 10, 2019): 579. http://dx.doi.org/10.3390/app9030579.

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Slope failure behaviour of noncohesive media with the consideration of gravity and ground excitations is examined using the two-dimensional combined finite–discrete element method (FDEM). The FDEM aims at solving large-scale transient dynamics and is particularly suitable for this problem. The method discretises an entity into a couple of individual discrete elements. Within each discrete element, the finite element method (FEM) formulation is embedded so that contact forces and deformation between and of these discrete elements can be predicted more accurately. Noncohesive media is simply modelled with assembly of individual discrete elements without cohesion, that is, no joint elements need to be defined. To validate the effectiveness of the FDEM modelling, two examples are presented and compared with results from other sources. The FDEM results on gravitational collapse of rectangular soil heap and landslide triggered by the Chi-Chi earthquake show that the method is applicable and reliable for the analysis of slope failure behaviour of noncohesive media through comparison with results from other known methods such as the smoothed particle hydrodynamics (SPH), the discrete element method (DEM) and the material point method (MPM).

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2

Hong, Tao, Dong Hui Wen, and Ju Long Yuan. "Optimising Shot Peening Parameters Using Finite Element and Discrete Element Analysis." Applied Mechanics and Materials 10-12 (December 2007): 493–97. http://dx.doi.org/10.4028/www.scientific.net/amm.10-12.493.

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Shot peening is a cold-work process in which a stream of small spherical shot is blasted against a metallic component to generate a high compressive residual stress regime at the surface of the target. This paper presents a computational modelling of the shot peening process, in which the finite element (FE) method was employed to study the elastic-plastic dynamic process of the shot impact on a metallic target, and the discrete element (DE) method was used to study the multiple particles dynamics. Statistical analyses of the shot impact data reveal the relationships between peening process parameters and peening intensity, which can be used to optimise these process parameters to produce an improved outcome.

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3

Zeng, Yuping, Zhifeng Weng, and Fen Liang. "Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem." Discrete Dynamics in Nature and Society 2020 (September 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/9464389.

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In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes.

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4

He, Haiyan, Kaijie Liang, and Baoli Yin. "A numerical method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation." International Journal of Modeling, Simulation, and Scientific Computing 10, no. 01 (February 2019): 1941005. http://dx.doi.org/10.1142/s1793962319410058.

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In this paper, we consider the finite element method for two-dimensional nonlinear modified time-fractional fourth-order diffusion equation. In order to avoid using higher order elements, we introduce an intermediate variable [Formula: see text] and translate the fourth-order derivative of the original problem into a second-order coupled system. We discretize the fractional time derivative terms by using the [Formula: see text]-approximation and discretize the first-order time derivative term by using the second-order backward differentiation formula. In the fully discrete scheme, we implement the finite element method for the spatial approximation. Unconditional stability of the fully discrete scheme is proven and its optimal convergence order is obtained. Numerical experiments are carried out to demonstrate our theoretical analysis.

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5

Taforel, P., M. Renouf, F. Dubois, and C. Voivret. "Finite Element-Discrete Element Coupling Strategies for the Modelling of Ballast-Soil Interaction." International Journal of Railway Technology 4, no. 2 (2015): 73–95. http://dx.doi.org/10.4203/ijrt.4.2.4.

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6

CHRISTIANSEN, SNORRE H. "A CHARACTERIZATION OF SECOND-ORDER DIFFERENTIAL OPERATORS ON FINITE ELEMENT SPACES." Mathematical Models and Methods in Applied Sciences 14, no. 12 (December 2004): 1881–92. http://dx.doi.org/10.1142/s0218202504003854.

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We describe all operators on scalar finite element spaces which appear as the restriction of a second-order (linear) differential operator. More precisely we provide a family of isomorphisms between this space of discrete differential operators and products of some exotic finite element spaces. This provides a unified framework for the Regge calculus of numerical relativity and the Nédélec edge elements of computational electromagnetism.

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7

An, Huaming, Hongyuan Liu, and Haoyu Han. "Hybrid Finite-Discrete Element Modelling of Excavation Damaged Zone Formation Process Induced by Blasts in a Deep Tunnel." Advances in Civil Engineering 2020 (July 16, 2020): 1–27. http://dx.doi.org/10.1155/2020/7153958.

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A brief literature review of numerical studies on excavation damage zone (EDZ) is conducted to compare the main numerical methods on EDZ studies. A hybrid finite-discrete element method is then proposed to model the EDZ induced by blasts. During the excavation by blasts, the rock mass around the borehole is subjected to dynamic loads, i.e., strong shock waves crushing the adjacent rocks and high-pressure gas expanding cracks. Therefore, the hybrid finite-discrete element method takes into account the transition of the rock from continuum to discontinuum through fracture and fragmentation, the detonation-induced gas expansion and flow through the fractured rock, and the dependence of the rock fracture dynamic behaviour on the loading rates. After that, the hybrid finite-discrete element method is calibrated by modelling the rock failure process in the uniaxial compression strength (UCS) test and Brazilian tensile strength (BTS) test. Finally, the hybrid finite-discrete element method is used to model the excavation process in a deep tunnel. The hybrid finite-discrete element method successfully modelled the stress propagation and the fracture initiation and propagation induced by blasts. The main components of the EDZ are obtained and show good agreements with those well documented in the literature. The influences of the initial gas pressure, in situ stress, and spacing between boreholes are discussed. It is concluded that the hybrid finite-discrete element method is a valuable numerical tool for studying the EDZ induced by blasts in deep tunnels.

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8

Ransing, R. S., D. T. Gethin, A. R. Khoei, P. Mosbah, and R. W. Lewis. "Powder compaction modelling via the discrete and finite element method." Materials & Design 21, no. 4 (August 2000): 263–69. http://dx.doi.org/10.1016/s0261-3069(99)00081-3.

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9

Choi, J. L., and D. T. Gethin. "A discrete finite element modelling and measurements for powder compaction." Modelling and Simulation in Materials Science and Engineering 17, no. 3 (February 17, 2009): 035005. http://dx.doi.org/10.1088/0965-0393/17/3/035005.

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10

Salgado, Abner J., and Wujun Zhang. "Finite element approximation of the Isaacs equation." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (March 2019): 351–74. http://dx.doi.org/10.1051/m2an/2018067.

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We propose and analyze a two-scale finite element method for the Isaacs equation. The fine scale is given by the mesh size h whereas the coarse scale ε is dictated by an integro-differential approximation of the partial differential equation. We show that the method satisfies the discrete maximum principle provided that the mesh is weakly acute. This, in conjunction with weak operator consistency of the finite element method, allows us to establish convergence of the numerical solution to the viscosity solution as ε, h → 0, and ε ≳ (h|log h|)1/2. In addition, using a discrete Alexandrov Bakelman Pucci estimate we deduce rates of convergence, under suitable smoothness assumptions on the exact solution.

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11

Joulin, Clément, Jiansheng Xiang, John-Paul Latham, Christopher Pain, and Pablo Salinas. "Capturing heat transfer for complex-shaped multibody contact problems, a new FDEM approach." Computational Particle Mechanics 7, no. 5 (February 22, 2020): 919–34. http://dx.doi.org/10.1007/s40571-020-00321-w.

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Abstract This paper presents a new approach for the modelling of heat transfer in 3D discrete particle systems. Using a combined finite–discrete element (FDEM) method, the surface of contact is numerically computed when two discrete meshes of two solids experience a small overlap. Incoming heat flux and heat conduction inside and between solid bodies are linked. In traditional FEM (finite element method) or DEM (discrete element method) approaches, to model heat transfer across contacting bodies, the surface of contact is not directly reconstructed. The approach adopted here uses the number of surface elements from the penetrating boundary meshes to form a polygon of the intersection, resulting in a significant decrease in the mesh dependency of the method. Moreover, this new method is suitable for any sizes or shapes making up the particle system, and heat distribution across particles is an inherent feature of the model. This FDEM approach is validated against two models: a FEM model and a DEM pipe network model. In addition, a multi-particle heat transfer contact problem of complex-shaped particles is presented.

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12

Makridakis, Ch G., and P. Monk. "Time-discrete finite element schemes for Maxwell's equations." ESAIM: Mathematical Modelling and Numerical Analysis 29, no. 2 (1995): 171–97. http://dx.doi.org/10.1051/m2an/1995290201711.

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13

Ambrosi, D. "A New Finite Element Scheme for the Boussinesq Equations." Mathematical Models and Methods in Applied Sciences 07, no. 02 (March 1997): 193–209. http://dx.doi.org/10.1142/s0218202597000128.

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In this paper we consider the Boussinesq equations to simulate the motion of water waves with a moderate curvature of the free surface. The mathematical model describing the wave dynamics is introduced together with a short description of its derivation, posing emphasis on the related assumptions. The discrete representation of the Boussinesq equations is faced with numerical difficulties of two kinds: the nonsymmetric character of the (nonlinear) advection–propagation operator and the presence of third-order differential terms accounting for dispersion phenomena. In this paper it is shown how it is possible to use a finite element Taylor–Galerkin method to discretize the equations, ensuring high order accuracy both in time and space and obtaining a numerical solution free of spurious oscillations.

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14

Chen, Xu Dong, Andrew H. C. Chan, and Jian Yang. "FEM/DEM Modelling of Hard Body Impact on the Laminated Glass." Applied Mechanics and Materials 553 (May 2014): 786–91. http://dx.doi.org/10.4028/www.scientific.net/amm.553.786.

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Laminated glass is widely used for structural members in industry. Among all loading types, impact is one of the most adverse forms due to its dynamic effect. In order to investigate how laminated glass fractures under hard body impact and the subsequent fragmentation, the combined finite-discrete element method (FEM/DEM) was employed in this paper. This method discretises a single discrete element in finite elements, giving a more accurate estimate of the contact forces and deformation of the elements. This paper presents the transient responses of a laminated glass beam under impact by using a simple mixed-mode (I + II) elasto-plastic fracture model developed for the FEM/DEM program. The results from this mixed-mode model has been compared and validated with that from Mode I fracture model. A parametric study on the laminated glass is performed based on the mixed-mode model, showing its better energy absorption capacity than monolithic glass and the influence of the interfacial strength on the damage behaviour, demonstrating that laminated glass is safer than the monolithic glass. It also shows that the FEM/DEM modelling and the new mixed-mode (I+II) model is applicable and provides realistic simulations.

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15

Kikidis, Dimitrios, and Athanasios Bibas. "A Clinically Oriented Introduction and Review on Finite Element Models of the Human Cochlea." BioMed Research International 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/975070.

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Due to the inaccessibility of the inner ear, direct in vivo information on cochlear mechanics is difficult to obtain. Mathematical modelling is a promising way to provide insight into the physiology and pathology of the cochlea. Finite element method (FEM) is one of the most popular discrete mathematical modelling techniques, mainly used in engineering that has been increasingly used to model the cochlea and its elements. The aim of this overview is to provide a brief introduction to the use of FEM in modelling and predicting the behavior of the cochlea in normal and pathological conditions. It will focus on methodological issues, modelling assumptions, simulation of clinical scenarios, and pathologies.

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16

Rabczuk, Timon. "Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives." ISRN Applied Mathematics 2013 (March 20, 2013): 1–38. http://dx.doi.org/10.1155/2013/849231.

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An overview of computational methods to model fracture in brittle and quasi-brittle materials is given. The overview focuses on continuum models for fracture. First, numerical difficulties related to modelling fracture for quasi-brittle materials will be discussed. Different techniques to eliminate or circumvent those difficulties will be described subsequently. In that context, regularization techniques such as nonlocal models, gradient enhanced models, viscous models, cohesive zone models, and smeared crack models will be discussed. The main focus of this paper will be on computational methods for discrete fracture (discrete cracks). Element erosion technques, inter-element separation methods, the embedded finite element method (EFEM), the extended finite element method (XFEM), meshfree methods (MMs), boundary elements (BEMs), isogeometric analysis, and the variational approach to fracture will be reviewed elucidating advantages and drawbacks of each approach. As tracking the crack path is of major concern in computational methods that preserve crack path continuity, one section will discuss different crack tracking techniques. Finally, cracking criteria will be reviewed before the paper ends with future research perspectives.

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17

GOUBET, OLIVIER. "BEHAVIOR OF SMALL FINITE ELEMENT STRUCTURES FOR THE NAVIER–STOKES EQUATIONS." Mathematical Models and Methods in Applied Sciences 06, no. 01 (February 1996): 1–32. http://dx.doi.org/10.1142/s021820259600002x.

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This article deals with the long-time behavior of the solution of the two-dimensional Navier–Stokes equations. At each time step, we use finite elements to split the solution into a large-scale component and a small-scale component, and we follow both components in time. Next, considering a mixed finite element approximation of the equations, we prove that many properties that hold for the exact solution extend to the discrete solution as well, uniformly in the discretization parameter.

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18

Cames-Pintaux, A. M., and M. Nguyen-Lamba. "Finite-Element Enthalpy Method for Discrete Phase Change." Numerical Heat Transfer, Part B: Fundamentals 9, no. 4 (1986): 403–17. http://dx.doi.org/10.1080/10407798608552146.

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19

Carstensen, Carsten, Dietmar Gallistl, and Jun Hu. "A discrete Helmholtz decomposition with Morley finite element functions and the optimality of adaptive finite element schemes." Computers & Mathematics with Applications 68, no. 12 (December 2014): 2167–81. http://dx.doi.org/10.1016/j.camwa.2014.07.019.

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20

Rousseau, Jessica, Philippe Marin, Laurent Daudeville, and Sergueï Potapov. "A discrete element/shell finite element coupling for simulating impacts on reinforced concrete structures." European Journal of Computational Mechanics 19, no. 1-3 (January 2010): 153–64. http://dx.doi.org/10.3166/ejcm.19.153-164.

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21

AURADA, MARKUS, JENS M. MELENK, and DIRK PRAETORIUS. "MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS." Mathematical Models and Methods in Applied Sciences 24, no. 01 (October 31, 2013): 113–44. http://dx.doi.org/10.1142/s0218202513500486.

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We introduce a stabilized conforming mixed finite element method for a macroscopic model in micromagnetics. We show well-posedness of the discrete problem for higher order elements in two and three dimensions, develop a full a priori analysis for lowest order elements, and discuss the extension of the method to higher order elements. We introduce a residual-based a posteriori error estimator and present an adaptive strategy. Numerical examples illustrate the performance of the method.

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22

Zhao, Jie, Hong Li, Zhichao Fang, and Xue Bai. "Numerical Solution of Burgers’ Equation Based on Mixed Finite Volume Element Methods." Discrete Dynamics in Nature and Society 2020 (March 19, 2020): 1–13. http://dx.doi.org/10.1155/2020/6321209.

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In this article, mixed finite volume element (MFVE) methods are proposed for solving the numerical solution of Burgers’ equation. By introducing a transfer operator, semidiscrete and fully discrete MFVE schemes are constructed. The existence, uniqueness, and stability analyses for semidiscrete and fully discrete MFVE schemes are given in detail. The optimal a priori error estimates for the unknown and auxiliary variables in the L2Ω norm are derived by using the stability results. Finally, numerical results are given to verify the feasibility and effectiveness.

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23

Szklennik, Paweł, and Grzegorz Bąk. "Numerical prediction of dynamic stability loss of a flexible cylindrical shell in a granular medium." Bulletin of the Military University of Technology 68, no. 3 (September 30, 2019): 159–68. http://dx.doi.org/10.5604/01.3001.0013.5563.

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The paper presents an application of the discrete element method for an analysis of dynamical stability loss of the flexible cylindrical shell section interacting with a model granular medium. The main scope was to investigate the forms of dynamical stability loss, considering finite displacements. The granular medium weight and additional external load transmitted from the surface were considered with different backfill height over the cylindrical shell. Application of a discrete model enables to consider random imperfections in the granular medium structure. It is shown that imperfections of a granular soil structure occurring in a close surrounding of the shell have an essential impact on the shell deformations. Numerical modelling, using the discrete element method, enables to obtain solutions of dynamic interaction by investigating finite two dimensional deformations. Keywords: discrete element method, cylindrical shell, granular medium, stability

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24

Chung, Y. C., and J. Y. Ooi. "Linking of discrete element modelling with finite element analysis for analysing structures in contact with particulate solid." Powder Technology 217 (February 2012): 107–20. http://dx.doi.org/10.1016/j.powtec.2011.10.016.

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25

Zhang, H., Y. J. Huang, Z. J. Yang, S. L. Xu, and X. W. Chen. "A discrete-continuum coupled finite element modelling approach for fibre reinforced concrete." Cement and Concrete Research 106 (April 2018): 130–43. http://dx.doi.org/10.1016/j.cemconres.2018.01.010.

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26

Abdelaziz, Aly, Qi Zhao, and Giovanni Grasselli. "Grain based modelling of rocks using the combined finite-discrete element method." Computers and Geotechnics 103 (November 2018): 73–81. http://dx.doi.org/10.1016/j.compgeo.2018.07.003.

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27

Miglietta, Paola Costanza, Evan C. Bentz, and Giovanni Grasselli. "Finite/discrete element modelling of reversed cyclic tests on unreinforced masonry structures." Engineering Structures 138 (May 2017): 159–69. http://dx.doi.org/10.1016/j.engstruct.2017.02.019.

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28

Labra, Carlos, Jerzy Rojek, and Eugenio Oñate. "Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter." Rock Mechanics and Rock Engineering 50, no. 3 (November 22, 2016): 621–38. http://dx.doi.org/10.1007/s00603-016-1133-7.

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29

CHIEN, C. S., and B. W. JENG. "SYMMETRY REDUCTIONS AND A POSTERIORI FINITE ELEMENT ERROR ESTIMATORS FOR BIFURCATION PROBLEMS." International Journal of Bifurcation and Chaos 15, no. 07 (July 2005): 2091–107. http://dx.doi.org/10.1142/s0218127405013319.

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We discuss efficient continuation algorithms for solving nonlinear eigenvalue problems. First, we exploit the idea of symmetry reductions and discretize the problem on a symmetry cell by the finite element method. Then we incorporate the multigrid V-cycle scheme in the context of continuation method to trace solution branches of the discrete problems, where the preconditioned Lanczos method is used as the relaxation scheme. Next, we apply the symmetry reduction technique to the two-grid finite element discretization scheme [Chien & Jeng, 2005] to solve some nonlinear eigenvalue problems in physical science. The two-grid centered difference discretization scheme described therein was also implemented for comparison. Sample numerical results are reported.

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30

Michnevič, Edvard. "A TOOL FOR MODAL ANALYSIS OF LAMINATED BENDING PLATES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 12, no. 4 (December 31, 2006): 319–25. http://dx.doi.org/10.3846/13923730.2006.9636409.

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A new finite element for modelling laminated bending plates was defined based on the effective triangular finite element of the discrete Kirchhoff's theory. The plates can be made of layers arranged in any order and consisting of different but orthotropic materials. The suggested finite element has 6 degrees of freedom in every node, i e 3 linear displacements and 3 rotations about the axis of coordinates. A mathematical model of the element describes stress and strain effects both in the plane of the element or perpendicular to it, except for shear. The suggested element can be used for calculating laminated plates or beams, not subjected to heavy shear stresses. Some numerical case studies are provided, while the results obtained are compared with the well‐known analytical and numerical solutions.

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31

Javanbakht, Zia, Wayne Hall, Amandeep Singh Virk, John Summerscales, and Andreas Öchsner. "Finite element analysis of natural fiber composites using a self-updating model." Journal of Composite Materials 54, no. 23 (March 24, 2020): 3275–86. http://dx.doi.org/10.1177/0021998320912822.

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The aim of the current work was to illustrate the effect of the fibre area correction factor on the results of modelling natural fibre-reinforced composites. A mesoscopic approach is adopted to represent the stochastic heterogeneity of the composite, i.e. a meso-structural numerical model was prototyped using the finite element method including quasi-unidirectional discrete fibre elements embedded in a matrix. The model was verified by the experimental results from previous work on jute fibres but is extendable to every natural fibre with cross-sectional non-uniformity. A correction factor was suggested to fine-tune both the analytical and numerical models. Moreover, a model updating technique for considering the size-effect of fibres is introduced and its implementation was automated by means of FORTRAN subroutines and Python scripts. It was shown that correcting and updating the fibre strength is critical to obtain accurate macroscopic response of the composite when discrete modelling of fibres is intended. Based on the current study, it is found that consideration of the effect of flaws on the strength of natural fibres and inclusion of the fibre area correction factor are crucial to obtain realistic results.

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32

Lilja, Ville-Pekka, Arttu Polojärvi, Jukka Tuhkuri, and Jani Paavilainen. "Effective material properties of a finite element-discrete element model of an ice sheet." Computers & Structures 224 (November 2019): 106107. http://dx.doi.org/10.1016/j.compstruc.2019.106107.

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33

Burman, Erik, Peter Hansbo, and Mats G. Larson. "Augmented Lagrangian finite element methods for contact problems." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 1 (January 2019): 173–95. http://dx.doi.org/10.1051/m2an/2018047.

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We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.

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34

Baraldi, Daniele, Giosuè Boscato, Claudia Brito de Carvalho Bello, Antonella Cecchi, and Emanuele Reccia. "Discrete and Finite Element Models for the Analysis of Unreinforced and Partially Reinforced Masonry Arches." Key Engineering Materials 817 (August 2019): 229–35. http://dx.doi.org/10.4028/www.scientific.net/kem.817.229.

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In this work the behavior of masonry arches, without reinforcement and with partial reinforcement, is investigated by means of three different numerical models. The first one is a Discrete Element model based on rigid blocks, and elastic-plastic interfaces; the second one is a standard heterogeneous Finite Element Model, which is adopted for a detailed micro-modelling of arch voussoirs, joints, and reinforcements. The third model is analytic-numerical, and it is adopted for validating the other numerical results. The aim of the work is the comparison and validation of the numerical Finite and Discrete Element models for the correct simulation of masonry arch behavior, together with the evaluation of the effectiveness of these models in simulating the behavior of the partially reinforced arch.

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35

BENSOW, RICKARD E., and MATS G. LARSON. "DISCONTINUOUS/CONTINUOUS LEAST-SQUARES FINITE ELEMENT METHODS FOR ELLIPTIC PROBLEMS." Mathematical Models and Methods in Applied Sciences 15, no. 06 (June 2005): 825–42. http://dx.doi.org/10.1142/s0218202505000595.

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Least-squares finite element methods (LSFEM) are useful for first-order systems, where they avoid the stability consideration of mixed methods and problems with constraints, like the div-curl problem. However, LSFEM typically suffer from requirements on the solution to be very regular. This rules out, e.g., applications posed on nonconvex domains. In this paper we study a least-squares formulation where the discrete space is enriched by discontinuous elements in the vicinity of singularities. The weighting on the interelement terms are chosen to give correct regularity of the solution space and thus making computation of less regular problems possible. We apply this technique to the first-order Poisson problem, show coercivity and a priori estimates, and present numerical results in 3D.

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36

Popescu, Ileana Nicoleta, and Ruxandra Vidu. "Compaction Behaviour Modelling of Metal-Ceramic Powder Mixtures. A Review." Scientific Bulletin of Valahia University - Materials and Mechanics 16, no. 14 (April 1, 2018): 28–37. http://dx.doi.org/10.1515/bsmm-2018-0006.

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Abstract Powder mixtures compaction behavior can be quantitatively expressed by densification equations that describe the relationship between densities - applied pressure during the compaction stages, using correction factors. The modelling of one phase (metal/ceramic) powders or two-phase metal-ceramic powder composites was studied by many researchers, using the most commonly compression equations (Balshin, Heckel, Cooper and Eaton, Kawakita and Lüdde) or relative new ones (Panelli - Ambrózio Filho, Castagnet-Falcão- Leal Neto, Ge Rong-de, Parilák and Dudrová, Gerdemann and Jablonski. Also, for a better understanding of the consolidation process by compressing powder blends and for better prediction of compaction behavior, it's necessary the modeling and simulation of the powder pressing process by computer numerical simulation. In this paper are presented the effect of ceramic particles additions in metallic matrix on the compressibility of composites made by P/M route, taking into account (a) the some of above mentioned powder compression equations and also (b) the compaction behavior modeling through finite element method (FEM) and discrete element modeling (DEM) or combined finite/ discrete element (FE/DE) method.

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37

Tosone, C., and A. Maceri. "The Clamped Plate with Elastic Unilateral Obstacles: A Finite Element Approach." Mathematical Models and Methods in Applied Sciences 13, no. 09 (September 2003): 1231–43. http://dx.doi.org/10.1142/s021820250300288x.

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We consider the problem of a clamped elastic thin plate unilaterally constrained by an elastic obstacle. A discrete, finite element approach to solve this nonlinear problem is given here and its convergence properties are discussed.

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38

Forti, Tiago, Gustavo Batistela, Nadia Forti, and Nicolas Vianna. "3D Mesoscale Finite Element Modelling of Concrete under Uniaxial Loadings." Materials 13, no. 20 (October 15, 2020): 4585. http://dx.doi.org/10.3390/ma13204585.

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Concrete exhibits a complex mechanical behavior, especially when approaching failure. Its behavior is governed by the interaction of the heterogeneous structures of the material at the first level of observation below the homogeneous continuum, i.e., at the mesoscale. Concrete is assumed to be a three-phase composite of coarse aggregates, mortar, and the interfacial transitional zone (ITZ) between them. Finite element modeling on a mesoscale requires appropriate meshes that discretize the three concrete components. As the weakest link in concrete, ITZ plays an important role. However, meshing ITZ is a challenging issue, due to its very reduced thickness. Representing ITZ with solid elements of such reduced size would produce very expensive finite element meshes. An alternative is to represent ITZ as zero-thickness interface elements. This work adopts interface elements for ITZ. Damage plasticity model is adopted to describe the softening behavior of mortar in compression, while cohesive fractures describe the cracking process. Numerical experiments are presented. First example deals with the estimation of concrete Young’s modulus. Experimental tests were performed to support the numerical test. A second experiment simulates a uniaxial compression test and last experiment simulates a uniaxial tensile test, where results are compared to data from the literature.

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Bangash, T., and A. Munjiza. "Experimental validation of a computationally efficient beam element for combined finite-discrete element modelling of structures in distress." Computational Mechanics 30, no. 5-6 (April 1, 2003): 366–73. http://dx.doi.org/10.1007/s00466-003-0412-9.

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Koleva, Miglena. "FINITE ELEMENT SOLUTION OF BOUNDARY VALUE PROBLEMS WITH NONLOCAL JUMP CONDITIONS." Mathematical Modelling and Analysis 13, no. 3 (September 30, 2008): 383–400. http://dx.doi.org/10.3846/1392-6292.2008.13.383-400.

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We consider stationary linear problems on non‐connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

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Jönsson, J., E. Svensson, and J. T. Christensen. "Strain gauge measurement of wheel-rail interaction forces." Journal of Strain Analysis for Engineering Design 32, no. 3 (April 1, 1997): 183–91. http://dx.doi.org/10.1243/0309324971513328.

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A theoretical basis for quasi static determination of wheel—rail interaction forces using strain measures in the foot of the rail is given. Vlasov's theory for thin-walled beams is used in combination with continuous translational and rotational elastic supports based on smoothing out the stiffness of the rail sleepers. The smoothing out of the rotational elastic support has traditionally not been done. The use of this model is validated by the decay lengths of the problem and through finite element analysis. The finite element analysis is performed using discrete sleeper stiffness and Vlasov beam elements. The sensitivity of the measuring technique to parameter variations is illustrated and an example shows the simplicity of the proposed direct measuring technique.

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Górniak, J., P. Villard, and P. Delmas. "Coupled discrete and finite-element modelling of geosynthetic tubes filled with granular material." Geosynthetics International 23, no. 5 (October 2016): 362–80. http://dx.doi.org/10.1680/jgein.16.00003.

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Liu, Hong Yuan. "Hybrid Finite-Discrete Element Modelling of Dynamic Fracture of Rocks with Various Geometries." Applied Mechanics and Materials 256-259 (December 2012): 183–86. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.183.

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The hybrid finite-discrete element method Y-2D/3D IDE is applied to model the dynamic fracture of rock specimens with various geometries during impacting a fixed rigid surface. It is found that the modelled primary fractures are highly dependent on the rock geometry determining the weakest plane for a given impact, which agrees well with others' experimental and SPH numerical results. Compared with others' SPH results, Y-2D/3D IDE better simulates the actinomorphic pattern of primary fractures around the impact area and the secondary & tertiary fractures observed in the dynamic fracture experiments. It is concluded that the proposed Y-2D/3D IDE is a valuable tool to model rock dynamic fracture compared with FEM and DEM.

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Yang, Z. J., and Jianfei Chen. "Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams." Engineering Fracture Mechanics 72, no. 14 (September 2005): 2280–97. http://dx.doi.org/10.1016/j.engfracmech.2005.02.004.

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Sharafisafa, Mansour, Akira Sato, Atsushi Sainoki, Luming Shen, and Zeinab Aliabadian. "Combined finite-discrete element modelling of hydraulic fracturing in deep geologically complex reservoirs." International Journal of Rock Mechanics and Mining Sciences 167 (July 2023): 105406. http://dx.doi.org/10.1016/j.ijrmms.2023.105406.

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Zhang, Yaping, Jiliang Cao, Weiping Bu, and Aiguo Xiao. "A fast finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 02 (March 27, 2020): 2050016. http://dx.doi.org/10.1142/s1793962320500166.

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In this work, we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. Finally, some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

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Kudela, Pawel, and Wiesław M. Ostachowicz. "Wave Propagation Modelling in Composite Plates." Applied Mechanics and Materials 9 (October 2007): 89–104. http://dx.doi.org/10.4028/www.scientific.net/amm.9.89.

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The paper presents results of numerical simulation for transverse elastic waves corresponding to A0 mode of Lamb waves propagating in a composite plate. This problem is solved by using the Spectral Finite Element Method. Spectral plate elements with 36 nodes defined at Gauss-Lobatto-Legendre points are used. As a consequence of selecting Lagrange polynomials discrete orthogonality guaranteed leading to a diagonal mass matrix. This results in a crucial reduction of numerical operations required for a chosen time integration scheme. Numerical calculations have been carried out for various orientations of reinforcing fibres within the plate as well as for various fibre volumes fractions. The paper shows that the velocities of transverse elastic waves in composite materials are functions of the fibre orientation and the fibre volume fraction.

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Tong, Mingming. "Review of Particle-Based Computational Methods and Their Application in the Computational Modelling of Welding, Casting and Additive Manufacturing." Metals 13, no. 8 (August 3, 2023): 1392. http://dx.doi.org/10.3390/met13081392.

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A variety of particle-based methods have been developed for the purpose of computationally modelling processes that involve, for example, complex topological changes of interfaces, significant plastic deformation of materials, fluid flow in conjunction with heat transfer and phase transformation, flow in porous media, granular flow, etc. Being different from the conventional methods that directly solve related governing equations using a computational grid, the particle-based methods firstly discretize the continuous medium into discrete pseudo-particles in mathematics. The methods then mathematically solve the governing equations by considering the local interaction between neighbouring pseudo-particles. Such solutions can reflect the overall flow, deformation, heat transfer and phase transformation processes of the target materials at the mesoscale and macroscale. This paper reviews the fundamental concepts of four different particle-based methods (lattice Boltzmann method—LBM, smoothed particle hydrodynamics—SPH, discrete element method—DEM and particle finite element method—PFEM) and their application in computational modelling research on welding, casting and additive manufacturing.

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Hou, Yaxin, Ruihan Feng, Yang Liu, Hong Li, and Wei Gao. "A MFE method combined with L1-approximation for a nonlinear time-fractional coupled diffusion system." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 01 (January 10, 2017): 1750012. http://dx.doi.org/10.1142/s179396231750012x.

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In this paper, a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element (MFE) method in space combined with L1-approximation and implicit second-order backward difference scheme in time. The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived. Finally, some numerical tests are shown to verify our theoretical analysis.

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Burman, Erik, Jonathan Ish-Horowicz, and Lauri Oksanen. "Fully discrete finite element data assimilation method for the heat equation." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 2065–82. http://dx.doi.org/10.1051/m2an/2018030.

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We consider a finite element discretization for the reconstruction of the final state of the heat equation, when the initial data is unknown, but additional data is given in a sub domain in the space time. For the discretization in space we consider standard continuous affine finite element approximation, and the time derivative is discretized using a backward differentiation. We regularize the discrete system by adding a penalty on the H2-semi-norm of the initial data, scaled with the mesh-parameter. The analysis of the method uses techniques developed in E. Burman and L. Oksanen [Numer. Math. 139 (2018) 505–528], combining discrete stability of the numerical method with sharp Carleman estimates for the physical problem, to derive optimal error estimates for the approximate solution. For the natural space time energy norm, away from t = 0, the convergence is the same as for the classical problem with known initial data, but contrary to the classical case, we do not obtain faster convergence for the L2-norm at the final time.

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