Developing a four-dimensional lattice spring model for mechanical responses of solids

Zhao, Gao‐Feng

doi:10.1016/j.cma.2016.11.034

Cited by 85 publications

(35 citation statements)

References 19 publications

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“…Under this condition, 4D‐LSM can reproduce the isotropic elastic responses. More details about 4D‐LSM can be found in Zhao's paper …”

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 98%

“…The 4D lattice model consists of the initial model, the parallel model, and the 4D interaction (spring). There are three types of 4D interactions (Figure C) that were given by Zhao . The first type is to connect the original mass point (A, for example) with its mapped point (A ′ ), and the spring stiffness is denoted by k α (Figure C, type A).…”

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 99%

“…For the 4D lattice model, the polynomial equation between Poisson's ratio ( ν ) and the 4D stiffness ratio ( λ ) can be given as follows:

λ^{4 D} = - 211.13493779 ν^{3} + 162.84655851 ν^{2} - 55.42449419 ν + 6.92902211 .

…”

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 99%

“…Detailed introduction of 4D‐LSM and the verification of elastic solutions have been given in the original literature . In this section, to verify the convergence of 4D‐LSM, a tunnel model (see Figure A) is built by 4D‐LSM, DLSM, and FEM.…”

Section: Convergence Of 4d‐lsmmentioning

confidence: 99%

“…Thereafter, many efforts were made to overcome this limitation, including the introduction of fourth‐dimensional interaction and multibody shear spring . The four‐dimensional LSM (4D‐LSM) was developed by Zhao by utilizing the extra dimension concept. Four‐dimensional LSM is more suitable for the geometric nonlinear problem because it is free from solving the polar decomposition like nonlinear finite element method (FEM) and the cumulative calculation of shear deformation in the discrete element method (DEM) .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Mechanical behavior of porous solid considering mesoscopic elastic buckling

Zhang

Zhao

2020

Num Anal Meth Geomechanics

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Summary In this work, the elastic buckling of porous solids was investigated using a lattice spring model (LSM). The capability of the LSM to solve elastic buckling problems was comprehensively verified by comparing well‐established numerical and analytical solutions. Following this, the buckling of a porous solid was studied, in which two porous structures were considered, ie, the random porous model and the Voronoi porous model. The results reveal that both the porosity and the shape of the pores influence the elastic buckling bearing capacity of the porous solid. Finally, the mechanical responses of a porous solid with an extra high porosity (0.85) were numerically investigated. Our numerical results demonstrated that the nonlinear elastic response of the porous solid might come from its mesoscale elastic buckling. This work shows the ability and promise of using the LSM as a fundamental numerical tool for the deep investigation of the buckling mechanical behavior of porous solids.

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“…Under this condition, 4D‐LSM can reproduce the isotropic elastic responses. More details about 4D‐LSM can be found in Zhao's paper …”

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 98%

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 99%

“…For the 4D lattice model, the polynomial equation between Poisson's ratio ( ν ) and the 4D stiffness ratio ( λ ) can be given as follows:

λ^{4 D} = - 211.13493779 ν^{3} + 162.84655851 ν^{2} - 55.42449419 ν + 6.92902211 .

…”

Section: Four‐dimensional Lattice Spring Modelmentioning

confidence: 99%

Section: Convergence Of 4d‐lsmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mechanical behavior of porous solid considering mesoscopic elastic buckling

Zhang

Zhao

2020

Num Anal Meth Geomechanics

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High‐performance computing of 3D blasting wave propagation in underground rock cavern by using 4D‐LSM on TianHe‐3 prototype E class supercomputer

Guo-jie

2022

Deep Underground Science and Engineering

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Parallel computing assigns the computing model to different processors on different devices and implements it simultaneously. Accordingly, it has broad applications in the numerical simulation of geotechnical engineering and underground engineering, of which models are always large-scale. With parallel computing, the computing time or the memory requirements will be reduced by splitting the original domain of the numerical model into many subdomains, which is thus named as the domain decomposition method. In this study, a cubic and equal volume domain decomposition strategy was utilized to realize the parallel computing on the distributed memory system of four-dimensional lattice spring model (4D-LSM) based on the message passing interface. With a more efficient communication strategy introduced, this study aimed at operating an one-billion-particle model on a supercomputer platform. The preprocessing procedure of the parallelized 4D-LSM was restructured and the particle generation strategy suitable for the supercomputer platform was employed to minimize the time consumption in preprocessing and calculation. On this basis, numerical calculations were performed on TianHe-3 prototype E class supercomputer at the National Supercomputer Center in Tianjin. Two fieldscale three-dimensional blasting wave propagation models were carried out, of which the numerical results verify the computing power and the advantage of the parallelized 4D-LSM in the simulation of large-scale three-dimension models. Subsequently, the time complexity and spatial complexity of 4D-LSM and other particle discrete element methods were analyzed.

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On the linear elastic responses of the 2D bonded discrete element model

Zhao

Yin

Russell

et al. 2018

Num Anal Meth Geomechanics

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Summary The bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solids in various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM which influence Poisson's ratio and Young's modulus, and accuracy when solving elastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticity analysis, and the distinct lattice spring model (DLSM) are compared in the investigation. It is shown that a shear interaction (local) factor and a geometric (global) factor are two essential elements for the 2D bonded DEM to reproduce a full range of Poisson's ratios. It is also found that the 2D bonded DEM might be unable to reproduce the correct displacements for elastic boundary value problems when the represented Poisson's ratio is close to 0.5 or the long‐range interaction is considered. In addition, an analytical relationship between the shear stiffness ratio and the Poisson's ratio, derived from a hyper elasticity analysis and applicable to discontinuum‐based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shown that the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.

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Developing a four-dimensional lattice spring model for mechanical responses of solids

Cited by 85 publications

References 19 publications

Mechanical behavior of porous solid considering mesoscopic elastic buckling

Mechanical behavior of porous solid considering mesoscopic elastic buckling

High‐performance computing of 3D blasting wave propagation in underground rock cavern by using 4D‐LSM on TianHe‐3 prototype E class supercomputer

On the linear elastic responses of the 2D bonded discrete element model

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