3D DDA Based on Variational Inequality Theory and Its Solution Scheme

2018 ◽  
Vol 15 (08) ◽  
pp. 1850081 ◽  
Author(s):  
W. Jiang ◽  
H. Zheng ◽  
G. H. Sun ◽  
W. Chen ◽  
P. C. Song
Keyword(s):  
Large Scale ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Numerical Instability ◽  
Contact Conditions ◽  
Inequality Theory ◽  
Discontinuous Deformation ◽  
Computation Scheme ◽  
New Formulation ◽  
Scale Matrix

The advantage of 3D discontinuous deformation analysis (3D DDA) is the rigorous contact conditions on the interaction of 3D blocks. These conditions are enforced by the penalty function convention; however, inappropriate penalty parameters easily generate numerical instability. To avoid the introduction of the penalty parameters, the contact conditions in 3D DDA are described as variational inequalities in this study, and the extra-gradient method is employed to solve this new formulation of 3D DDA. The proposed computation scheme is more flexible and dispenses with large scale matrix inversion. Some practical examples originally designed by Shi are analysed, verifying the effectiveness and precision of the new scheme.

DISCONTINUOUS DEFORMATION ANALYSIS BASED ON VARIATIONAL INEQUALITY THEORY

2011 ◽  
Vol 08 (02) ◽  
pp. 193-208 ◽  
Author(s):  
WEI JIANG ◽  
HONG ZHENG
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Penalty Function Method ◽  
Weak Nonlinearity ◽  
Contact Conditions ◽  
Inequality Theory ◽  
Discontinuous Deformation ◽  
Dda Method

In the conventional discontinuous deformation analysis (DDA) method, the contact conditions are enforced by the penalty function method. Improperly selected penalty parameters might cause numerical problems. In order to evade the introduction of the penalty parameters and to avoid "open–close iteration" that can not assure convergence, this study reformulates the DDA as a variational inequality problem. Based on the fact that the solution of a variational inequality is a fixed point of a natural projection map, the problem is reduced to the solution of nonsmooth equations with weak nonlinearity. Then, the Path Newton Method (PNM) is utilized to solve the equations. Some practical examples originally designed by Shi are reanalyzed, which demonstrates that the new DDA method is feasible.

An Efficient Contact Search Algorithm for Three-Dimensional Sphere Discontinuous Deformation Analysis

2020 ◽  
pp. 2050044
Author(s):  
Ganghai Huang ◽  
Yuanzhen Xu ◽  
Xiaofeng Chen ◽  
Jianjun Ma ◽  
Shu Zhang
Keyword(s):  
Data Structure ◽  
Large Scale ◽  
Search Algorithm ◽  
Three Dimensional ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Dimensional Sphere ◽  
Contact Search ◽  
Direct Search Algorithm ◽  
Discontinuous Deformation

The efficiency of contact search is one of the key factors related to the computational efficiency of three-dimensional sphere discontinuous deformation analysis (3D SDDA). This paper proposes an efficient contact search algorithm, called box search algorithm (BSA), for 3D SDDA. The implementation steps and data structure for BSA are designed, with a case study being conducted to verify its efficiency. The data structure also has been improved for parallelizing the computation in contact search. For the demonstration of the proposed algorithm (BSA), six cases with various sphere numbers are simulated. Simulation results show that the time consumed in contact search using BSA (CTofBSA) is much less than that by the direct search algorithm (DSA) (CTofDSA). For the case with 12,000 spheres, CTofBSA is 1.1[Formula: see text]h, which is only 1.3% of CTofDSA (84.62[Formula: see text]h). In addition, the proportion of the computation quantity of contact search in the entire computation (Pcs) is 91.3% by using DSA, while this value by BSA is only 12.4%, which demonstrates the contribution of BSA. The efficiency brought about by BSA (time consumed and computation quantity) may enable 3D SDDA to simulate large-scale problems.

scholarly journals Discontinuous Deformation Analysis Based on Wachspress Interpolation Function for Detailed Stress Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
W. Jiang ◽  
Y. H. Wang ◽  
G. H. Sun ◽  
P. C. Song ◽  
C. Mao
Keyword(s):  
Stress Distribution ◽  
Displacement Function ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Stress Distributions ◽  
Block Movement ◽  
Discontinuous Deformation ◽  
Movement And Deformation ◽  
New Formulation ◽  
Dda Method

In the original discontinuous deformation analysis (DDA) method, the complete first-order displacement function is used to describe block movement and deformation, which induce constant stress and strain throughout the block. To achieve a more detailed stress distribution, Wachspress interpolation displacement function is employed to express the displacement of blocks in DDA, and the interactions between blocks are still governed under the original DDA. Displacements of the vertexes of all blocks constitute new freedom vectors, and the stiffness and force matrix formulations are derived again. In the new formulation, Wachspress interpolation ensures that the edges of the blocks are straight; therefore, contact detection can be processed based on the original DDA. Several classical examples are analyzed. The results show that the new formulation obtains similar configurations as the original DDA but provides more detailed and continuous stress distributions within block element.

scholarly journals Numerical modeling of complex hydraulic fracture networks based on the discontinuous deformation analysis (DDA) method

2021 ◽  
pp. 014459872098153
Author(s):  
Yanzhi Hu ◽  
Xiao Li ◽  
Zhaobin Zhang ◽  
Jianming He ◽  
Guanfang Li
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fracture Network ◽  
Discontinuous Deformation Analysis ◽  
Deformation Analysis ◽  
Fracture Networks ◽  
Proposed Model ◽  
Discontinuous Deformation ◽  
Shale Reservoirs ◽  
Dda Method

Hydraulic fracturing is one of the most important technologies for shale gas production. Complex hydraulic fracture networks can be stimulated in shale reservoirs due to the existence of numerous natural fractures. The prediction of the complex fracture network remains a difficult and challenging problem. This paper presents a fully coupled hydromechanical model for complex hydraulic fracture network propagation based on the discontinuous deformation analysis (DDA) method. In the proposed model, the fracture propagation and rock mass deformation are simulated under the framework of DDA, and the fluid flow within fractures is simulated using lubrication theory. In particular, the natural fracture network is considered by using the discrete fracture network (DFN) model. The proposed model is widely verified against several analytical and experimental results. All the numerical results show good agreement. Then, this model is applied to field-scale modeling of hydraulic fracturing in naturally fractured shale reservoirs. The simulation results show that the proposed model can capture the evolution process of complex hydraulic fracture networks. This work offers a feasible numerical tool for investigating hydraulic fracturing processes, which may be useful for optimizing the fracturing design of shale gas reservoirs.

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