Featured Cover Fan, Huo; Huang, Duruo; Wang, Gang
International journal for numerical methods in engineering,
09/2020, Volume:
121, Issue:
18
Journal Article
Peer reviewed
Open access
The cover image is based on the Original Article Discontinuous deformation analysis handling vertex‐vertex contact based on principle of least effort by Duruo Huang et al., ...https://doi.org/10.1002/nme.6427.
Three‐dimensional discontinuous deformation analysis method (3D.DDA) is a dynamic calculation method based on the implicit solution. Inertial force is introduced in the solution process to ensure ...that the time variable is the real time variable, and springs are applied at the block boundary to avoid mutual intrusion between blocks. Therefore, the value of time step and contact spring stiffness directly affect the accuracy of 3D.DDA calculation results. Firstly, we analyzed the effects of the time step and contact spring stiffness on the numerical calculation results of the 3D.DDA method based on the theoretical formula derivation. Secondly, we studied the influence mechanism of time step on the simulation results of the 3D.DDA method individually based on the double block free falling model. And we determined the reasonable value area of time step. Then, considering the contacts between blocks, we studied the joint influence mechanism of time step and contact spring stiffness on the 3D.DDA simulation results based on the double block sliding model. And we analyzed the error between the 3D.DDA simulation value and the theoretical value under the conditions of different time step and contact spring stiffness. Based on that, we divided the combined value area of time step and contact spring stiffness into four regions (Q1, Q2, Q3, and Q4) and determined the optimal value area of time step and contact spring stiffness. At last, we carried out the slope rockfall model experiment and numerical simulation, and the trajectory of the falling rock in the numerical simulation was basically consistent with the experiment results, which verified the effectiveness of the optimal value area of time step and contact spring stiffness. The research results can provide a reference for the choice of the value of time step and contact spring stiffness in the numerical simulation based on the 3D.DDA method.
The three-dimensional discontinuous deformation analysis (3D-DDA) method was developed for the deformation simulation of rock block system cut by the natural discontinuities in rock mass engineering. ...In the conventional DDA, open-close iteration is used to deal with the contact constraints, which needs to apply or remove the normal or tangential springs repeatedly to meet the equilibrium equations at each time step. DDA provides a time step adjustment strategy to meet the fast convergence of open-close iterations, but when solving large-scale problems, the adjusted time step often reaches a very small order of magnitude, which makes the calculation time-consuming increase sharply. In the framework of the original 3D-DDA, a new contact potential based three-dimensional discontinuous deformation analysis method (3D-CPDDA) is developed. The proposed method not only retains the advantage of the original DDA method in defining local displacement functions on a single patch, but also integrates the simplicity and rapidity of potential based contact processing. The improved method is easier to be implemented in the parallel way, which can further improve the computational efficiency. Numerical examples have confirmed the correctness and feasibility of the proposed procedure.
An effective updated Lagrangian (UL) algorithm is designed for extending the recent distortion‐tolerant unsymmetric 8‐node, 24‐DOF hexahedral solid‐shell element, US‐ATFHS8, to finite deformation ...analysis of hyper‐elastic shell structures. The distinguishing feature of this unsymmetric element is that two different interpolation schemes are employed for virtual displacement and real stress calculations, respectively. The assumed natural strain (ANS) method with shell assumptions, referring to the current configuration, is introduced to modify the strain tensors derived from the assumed virtual displacement fields in terms of isoparametric coordinates, thereby mitigating shear locking and trapezoidal locking. On the other hand, the analytical trial functions (ATFs) derived from the general solutions of homogenous governing equations for linear elasticity are updated in each increment step to obtain the incremental deformation gradient, which is then utilized for calculating the real stresses for curing the numerical difficulties in large deformation problems. Numerical examples show that the proposed algorithm enables the hyper‐elastic solid‐shell element US‐ATFHS8 to exhibit excellent performance in both regular and distorted meshes and yield considerable results even when other models cannot work.
Summary
We present a generalized contact computation model for arbitrarily shaped polyhedra to simplify the contact analysis in discontinuous deformation analysis. A list of generalized contact ...constraints can be established for contacting polyhedra during contact detection. Each contact constraint contains information for 2 contact points, unique contact plane, and related contact modes (open, locked, or sliding). Computational aspects of the generalized contact model include identification of contact positions and contact modes, uniform penalty formulation of generalized contact constraint, and uniform updating of contact modes and contact planes in the open‐close iteration. Compared with previous strategies, the generalized contact computation model has a simpler data structure and fewer memory requirements. Meanwhile, it simplifies the penalty formulation and facilitates the open‐close iteration check while producing enough accuracy. Illustrative examples show the ability of the method to handle the full range of polyhedral shapes.
Summary
The efficiency of solving equations plays an important role in implicit‐scheme discontinuous deformation analysis (DDA). A systematic investigation of six iterative methods, namely, symmetric ...successive over relaxation (SSOR), Jacobi (J), conjugate gradient (CG), and three preconditioned CG methods (ie, J‐PCG, block J‐PCG BJ‐PCG, and SSOR‐PCG), for solving equations in three‐dimensional sphere DDA (SDDA) is conducted in this paper. Firstly, simultaneous equations of the SDDA and iterative formats of the six solvers are presented. Secondly, serial and OpenMP‐based parallel computing numerical tests are done on a 16‐core PC, the result of which shows that (a) for serial computing, the efficiency of the solvers is in this order: SSOR‐PCG > BJ‐PCG > J‐PCG > SSOR>J > CG, while for parallel computing, BJ‐PCG is the best solver; and (b) CG is not only the most sensitive to the ill‐condition of the equations but also the most time consuming under both serial and parallel computing. Thirdly, to estimate the effects of equation solvers acting on SDDA computations, an application example with 10 000 spheres and 200 000 calculation steps is simulated on this 16‐core PC using serial and parallel computing. The result shows that SSOR‐PCG is about six times faster than CG for serial computing, while BJ‐PCG is about four times faster than CG for parallel computing. On the other hand, the whole computation time using BJ‐PCG for parallel computing is 3.37 hours (ie, 0.061 s per step), which is about 36 times faster than CG for serial computing. Finally, some suggestions are given based on this investigation result.
AbstractIn the traditional discontinuous deformation analysis (DDA) method, the implicit time integration scheme is used to integrate equations of motion for modeling the mechanical behavior of a ...highly discrete rock block system. This requires that global equations be constantly solved. Hence, the computational efficiency of the traditional DDA method will decrease, especially when large-scale discontinuous problems are involved. Based on the explicit time integration scheme, an explicit version of the DDA (EDDA) method is proposed to improve computational efficiency of the traditional DDA method. Since a lumped mass matrix is used, there is no need to assemble global mass and stiffness matrices. More importantly, solving large-scale simultaneous algebraic equations can be avoided. The open–close iteration, which can assure the correct arrangement of constraints, is kept in the EDDA method. In addition, the simplex integration method, which is capable of conducting exact integration over an arbitrarily shaped block, is employed. Two numerical examples, including a sliding problem with an analytical solution and an underground cavern, are solved. The numerical results indicate the accuracy and robustness of the proposed EDDA method.
Starting from the recently-discovered TT¯\ \mathrm{T}\overline{\mathrm{T}} \-perturbed Lagrangians, we prove that the deformed solutions to the classical EoMs for bosonic field theories are ...equivalent to the unperturbed ones but for a specific field-dependent local change of coordinates. This surprising geometric outcome is fully consistent with the identification of TT¯\ \mathrm{T}\overline{\mathrm{T}} \-deformed 2D quantum field theories as topological JT gravity coupled to generic matter fields. Although our conclusion is valid for generic interacting potentials, it first emerged from a detailed study of the sine-Gordon model and in particular from the fact that solitonic pseudo-spherical surfaces embedded in ℝ3 are left invariant by the deformation. Analytic and numerical results concerning the perturbation of specific sine-Gordon soliton solutions are presented.
The seismic sliding of rock masses is an important phenomenon that is widely involved in earthquake geological hazards. Practical seismic sliding is a three‐dimensional problem, namely, the seismic ...loads may act in any direction and the rock masses may move in an arbitrary direction relative to the sliding plane. In the present work, the functions of two different seismic loading methods, that is, loading as body force time histories to the sliders or as displacement time histories to the base, are added to the program of the three‐dimensional discontinuous deformation analysis (3D‐DDA) method that is based on the contact theory to study the seismic sliding of rock blocks. The theoretical solutions of single‐block sliding on an incline under the two seismic loading methods are derived. By comparing the 3D‐DDA results of single‐block seismic sliding with the corresponding theoretical results, and comparing the 3D‐DDA results of seismic sliding of three‐stacked‐blocks under the two seismic loading methods, the correctness of 3D‐DDA for seismic sliding simulations is validated. Thereafter, the influence of three‐dimensional seismic components on single‐block sliding, and the movement of block groups under different seismic load conditions are investigated by 3D‐DDA simulations, which indicate the importance to consider rock mass seismic sliding as a three‐dimensional problem and the capability of 3D‐DDA for its analysis. This work builds a meaningful basis for the further numerical simulation study on the earthquake‐induced rock mass movements by 3D‐DDA.
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