Discontinuous deformation analysis with second-order finite element meshed block

Grayeli, Roozbeh; Mortazavi, Ali

doi:10.1002/nag.538

Cited by 27 publications

(30 citation statements)

References 12 publications

(12 reference statements)

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“…Clatworthy and Scheele [20] proposed sub-meshing to enhance block deformability. Grayeli and Mortazavi [21] developed a new 2-D DDA method using the six-node triangular elements and achieved a very good agreement between the analytical and numerical results produced by the modified DDA.…”

Section: Introductionmentioning

confidence: 72%

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Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

Beyabanaki

Jafari

Biabanaki

et al. 2009

Computers and Geotechnics

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Section: Introductionmentioning

confidence: 72%

“…In 2-D, Grayeli and Mortazavi [21] modified DDA using the high-order triangular finite elements. The basic three-dimensional elements in finite element method (FEM) are the tetrahedron element and the hexahedron element [37].…”

Section: Merging Finite Element Mesh Into a Blockmentioning

confidence: 99%

Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

Beyabanaki

Jafari

Biabanaki

et al. 2009

Computers and Geotechnics

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“…six-noded) triangular elements which are suitable to simulate blocks of any arbitrary shape. Grayeli and Mortazavi (2006) verified their implementation against the Kirsch solution for the displacement field around a circular cavity in an infinite elastic medium. Their results indicated that their DDA approach predicted the elastic deformations around the circular cavity with reasonable accuracy.…”

Section: Introductionmentioning

confidence: 96%

“…Grayeli and Mortazavi (2006) as well as Grayeli and Hatami (2008) present the finite element derivations for the implementation of FEM/DEM in DDA. In this formulation, the blocks are discretised internally using linear elastic, quadratic (i.e.…”

Section: Introductionmentioning

confidence: 99%

Elastic–plastic discontinuous deformation analysis using Mohr–Coulomb model

Mikola

Hatami

Doolin³

2011

Mining Technology

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The original (i.e. first order) discontinuous deformation analysis (DDA) formulation has two main shortcomings. First, a linear function is used to represent the displacement field in the blocks. This formulation implies that the state of stress (and strain) within each block is constant. Second, the material within each block is assumed as linear elastic. These two major limitations can often render the original DDA analysis method unrealistic and significantly inaccurate. In the modified DDA approach introduced in this study, these two limitations have been addressed. The authors have used the finite element method (FEM) to discretise each block in the DDA formulation using an automatic mesh generation algorithm to determine the distributions of stress and strain within each block to a desired accuracy. In addition, the Mohr-Coulomb elastic-plastic yield criterion is incorporated within the modified DDA analysis method using a time marching algorithm to account for the possibility of material failure. This allows the plastic behaviour (i.e. yielding) of the material within each block be included in the analysis, which is a significant improvement over the original DDA method. The numerical implementation of the Mohr-Coulomb criterion involves trials using initial elastic stress increment and comparisons with the yield criterion within each element. The proposed DDA formulation including the Mohr-Coulomb failure criterion (termed here as the MC-DDA method) is validated against selected analytical solutions, numerical solutions from FLAC verification problems and field measurements.

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“…One method is to glue small blocks together to form a larger block using artificial joints [3][4][5] and sub-blocks [6][7][8]. Some researchers added finite element meshes to the blocks so that stress variations within the blocks can be accounted for [9][10][11][12]. Moreover, Shi's recent development, the numerical manifold method (NMM), was aimed at describing stress distributions within the 1524 S. A. R. BEYABANAKI, A. JAFARI AND M. R. YEUNG…”

Section: Introductionmentioning

confidence: 99%

High‐order three‐dimensional discontinuous deformation analysis (3‐D DDA)

Beyabanaki

Jafari

Yeung

2009

Numer Methods Biomed Eng

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Three-dimensional discontinuous deformation analysis (3-D DDA) with high-order displacement functions has been derived for the requirement of highly accurate stress and strain calculations. The high-order displacement function allows nonlinear distributions of stresses and strains within a discrete block, which significantly enhances 3-D DDA as an analysis technique. Formulations of stiffness and force matrices in second-and third-order 3-D DDA due to elastic stress, initial stress, body force, point load, fixed point, inertial force, normal and shear contact forces and friction force are presented. The VC++ codes for the second-and third-order cases have been developed, and they have been applied to examples of 3-D beams, bending under various loading conditions applied at the end and to an example of discontinuous problem. Results of modeling, are well in agreement with theoretical solutions. In contrast, the results calculated for the same model, using original first-order 3-D DDA are far from the theoretical solutions.blocks [13,14]. The NMM, still retaining most of the DDA's attractive features, can be considered a generalized finite element and DDA method. Additionally, Chen et al. developed the high-order version of the manifold method [15] and Cheng et al. [16] showed that the use of more advanced Wilson non-conforming element in NMM can be useful in obtaining more accurate results for simple covers. Cheng and Zhang [17] presented three-dimensional NMM based on tetrahedron and hexahedron elements.An alternative approach is to include more polynomial terms in the displacement function. Unlike the sub-blocking method, it is possible to obtain good results using high-order displacement functions without discretizing the blocks. In the sub-blocking method, constraints between subblocks may not be satisfied accurately, which may lead to some errors in results, but this source of error is avoided in higher-order methods. The number of unknowns of analysis for one block using third-order displacement function is equal to the unknowns of analysis for a block divided into five sub-blocks. Using the sub-blocking method, to obtain good results comparable those from using a third-order displacement function, it is usually necessary to divide a block to many sub-blocks; however, the accuracy is problem dependent. Chern et al. [18] and Koo et al. [19] implemented a second-order displacement function in 2-D DDA. Ma et al. [20] and Koo and Chern [21] implemented a third-order displacement function in 2-D DDA method. Hsuing [22] developed a more general formulation for 2-D DDA. These studies showed that complicated stress and strain fields can be modeled using high-order displacement functions. MacLaughlin and Doolin [23] provided a review of more than 100 published and unpublished validation studies on the DDA approach. Previous DDA studies focused on solving problems in two dimensions, but in many engineering problems, three-dimensional effects have to be considered. Up to now, relatively little work on DDA development ...

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Discontinuous deformation analysis with second-order finite element meshed block

Cited by 27 publications

References 12 publications

Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

Elastic–plastic discontinuous deformation analysis using Mohr–Coulomb model

High‐order three‐dimensional discontinuous deformation analysis (3‐D DDA)

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