A numerical technique is described for the analysis of multiple interacting deformable bodies undergoing large displacements and rotations. Each body is considered an individual…
Abstract
A numerical technique is described for the analysis of multiple interacting deformable bodies undergoing large displacements and rotations. Each body is considered an individual discrete unit, which is idealized by a finite element model. Discrete finite element models interact with their surroundings through contact stresses, which are continually updated as the elements move and deform. The method of analysis consists of a finite element formulation based on a generalized explicit updated Lagrangian method. This formulation is a general finite element formulation, that permits the large deformation analysis of both continuum and discontinuum systems. Different validations of the proposed method of analysis, including cases that involve very large rotations, as well as some examples that demonstrate the application of the discrete finite element method to problems in rock mechanics are presented and discussed in the paper.
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Dawei Zhao, Erfan G. Nezami, Youssef M.A. Hashash and Jamshid Ghaboussi
Develop a new three‐dimensional discrete element code (BLOKS3D) for efficient simulation of polyhedral particles of any size. The paper describes efficient algorithms for the most…
Abstract
Purpose
Develop a new three‐dimensional discrete element code (BLOKS3D) for efficient simulation of polyhedral particles of any size. The paper describes efficient algorithms for the most important ingredients of a discrete element code.
Design/methodology/approach
New algorithms are presented for contact resolution and detection (including neighbor search and contact detection sections), contact point and force detection, and contact damping. In contact resolution and detection, a new neighbor search algorithm called TLS is described. Each contact is modeled with multiple contact points. A non‐linear force‐displacement relationship is suggested for contact force calculation and a dual‐criterion is employed for contact damping. The performance of the algorithm is compared to those currently available in the literature.
Findings
The algorithms are proven to significantly improve the analysis speed. A series of examples are presented to demonstrate and evaluate the performance of the proposed algorithms and the overall discrete element method (DEM) code.
Originality/value
Long computational times required to simulate large numbers of particles have been a major hindering factor in extensive application of DEM in many engineering applications. This paper describes an effort to enhance the available algorithms and further the engineering application of DEM.
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Application of the discrete element method (DEM) to real scale engineering problems involving three‐dimensional modelling of large, non‐spherical particles must consider the…
Abstract
Application of the discrete element method (DEM) to real scale engineering problems involving three‐dimensional modelling of large, non‐spherical particles must consider the inertia tensor and temporal change in the orientation of the particles when calculating the rotational motion. This factor has commonly been neglected in discrete element modelling although it will significantly influence the dynamic behaviour of non‐spherical particles. In this paper two methods, vector transformation and tensor transformation, for calculation of the rotational motion of particles in response to applied moments are presented. The methods consider the inertia tensor and the local object frame of arbitrary shaped particles and suggest solutions for the non‐linear Euler equations for calculation of their rotational motion. They are discussed with respect to implementation into a discrete element code and assessed in terms of their accuracy and computational efficiency.
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J.P. Morris, M.B. Rubin, S.C. Blair, L.A. Glenn and F.E. Heuze
We present the preliminary results from a parameter study investigating the stability of underground structures in response to explosion‐induced strong ground motions. In…
Abstract
We present the preliminary results from a parameter study investigating the stability of underground structures in response to explosion‐induced strong ground motions. In practice, even the most sophisticated site characterization may lack key details regarding precise joint properties and orientations within the rock mass. Thus, in order to place bounds upon the predicted behavior of a given facility, an extensive series of simulations representing different realizations may be required. The influence of both construction parameters (reinforcement, rock bolts, liners) and geological parameters (joint stiffness, joint spacing and orientation, and tunnel diameter to block size ratio) must be considered. We discuss the distinct element method (DEM) with particular emphasis on techniques for achieving improved computational efficiency, including the handling of contact detection and approaches to parallelization. We introduce a new approach for simulating deformation of the discrete blocks using the theory of a Cosserat point, which does not require internal discretization of the blocks. We also outline the continuum techniques we employ to obtain boundary conditions for the distinct element simulations. We present results from simulations of dynamic loading of several generic subterranean facilities in hard rock, demonstrating the suitability of the DEM for this application. These results demonstrate the significant role that joint geometry plays in determining the response of a given facility.
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When simulating the behaviour of granular assemblies and multi‐body systems using a discrete element analysis, the shape representation of the bodies and the contact detection…
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When simulating the behaviour of granular assemblies and multi‐body systems using a discrete element analysis, the shape representation of the bodies and the contact detection algorithm greatly influence the flexibility, accuracy and efficiency of the simulation. Several geometrical shape descriptors of two and three dimensional arbitrary rigid bodies are reviewed and a flexible 3‐D descriptor introduced. The aim is to identify appropriate shape descriptors which allow a variety of types of bodies to be investigated while ensuring accurate and efficient detection of inter‐particle contacts. Polygons/polyhedrons, and continuous and discrete function representations are examined. The investigation favours discrete representations due to their efficiency and flexibility, but illustrates the elegance and efficiency of using a continuous function representation, e.g. a superquadric, to generate the discrete representation and simplify the contact detection process.
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Xiao‐Jun Wang and Ted Belytschko
A hexahedral 8‐node element based on the Hellinger—Reissner principle is formulated with the γ projection operator so that it can achieve engineering accuracy for plate and beam…
Abstract
A hexahedral 8‐node element based on the Hellinger—Reissner principle is formulated with the γ projection operator so that it can achieve engineering accuracy for plate and beam problems with a single layer of elements. It passes the patch test and is less sensitive to mesh shape since the local coordinates are used to describe the stress fields. The resulting element stiffness is simple and only 3×3 submatrix inversions are needed. Numerical results show that the new element is both accurate and efficient.
Alireza Ahangar Asr, Asaad Faramarzi and Akbar A. Javadi
This paper aims to develop a unified framework for modelling triaxial deviator stress – axial strain and volumetric strain – axial strain behaviour of granular soils with the…
Abstract
Purpose
This paper aims to develop a unified framework for modelling triaxial deviator stress – axial strain and volumetric strain – axial strain behaviour of granular soils with the ability to predict the entire stress paths, incrementally, point by point, in deviator stress versus axial strain and volumetric strain versus axial strain spaces using an evolutionary-based technique based on a comprehensive set of data directly measured from triaxial tests without pre-processing. In total, 177 triaxial test results acquired from literature were used to develop and validate the models. Models aimed to not only be capable of capturing and generalising the complicated behaviour of soils but also explicitly remain consistent with expert knowledge available for such behaviour.
Design/methodology/approach
Evolutionary polynomial regression (EPR) was used to develop models to predict stress – axial strain and volumetric strain – axial strain behaviour of granular soils. EPR integrates numerical and symbolic regression to perform EPR. The strategy uses polynomial structures to take advantage of favourable mathematical properties. EPR is a two-stage technique for constructing symbolic models. It initially implements evolutionary search for exponents of polynomial expressions using a genetic algorithm (GA) engine to find the best form of function structure; second, it performs a least squares regression to find adjustable parameters, for each combination of inputs (terms in the polynomial structure).
Findings
EPR-based models were capable of generalising the training to predict the behaviour of granular soils under conditions that have not been previously seen by EPR in the training stage. It was shown that the proposed EPR models outperformed ANN and provided closer predictions to the experimental data cases. The entire stress paths for the shearing behaviour of granular soils using developed model predictions were created with very good accuracy despite error accumulation. Parametric study results revealed the consistency of developed model predictions, considering roles of various contributing parameters, with physical and engineering understandings of the shearing behaviour of granular soils.
Originality/value
In this paper, an evolutionary-based data-mining method was implemented to develop a novel unified framework to model the complicated stress-strain behaviour of saturated granular soils. The proposed methodology overcomes the drawbacks of artificial neural network-based models with black box nature by developing accurate, explicit, structured and user-friendly polynomial models and enabling the expert user to obtain a clear understanding of the system.
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M.F. SNYMAN, W.W. BIRD and J.B. MARTIN
The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. Sliding of the joint is assumed to be governed…
Abstract
The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. Sliding of the joint is assumed to be governed by Coulomb friction, with a non‐associated flow rule and no cohesion. The constitutive equations are formulated in a manner appropriate for a backward difference discretization in time along the path of loading. It is shown that the backward difference assumption can lead to an explicit formulation in which no essential distinction need be drawn between opening and closing of the joint and sliding when the joint is closed. However, an inherent limitation of the dilatant Coulomb model becomes evident; the final formulation is internally consistent but does not describe reversed shear displacement in a physically reasonable way. Explicit equations for the consistent tangent stiffness and for the corrector step (or return algorithm) of the standard Newton—Raphson iterative algorithm are given. The equations have been implemented as a user element in the finite element code ABAQUS, and illustrative examples are given.
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Joze Korelc and Peter Wriggers
Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and…
Abstract
Considers the problem of stability of the enhanced strain elements in the presence of large deformations. The standard orthogonality condition between the enhanced strains and constant stresses ensures satisfaction of the patch test and convergence of the method in case of linear elasticity. However, this does not hold in the case of large deformations. By analytic derivation of the element eigenvalues in large strain states additional orthogonality conditions can be derived, leading to a stable formulation, regardless of the magnitude of deformations. Proposes a new element based on a consistent formulation of the enhanced gradient with respect to new orthogonality conditions which it retains with four enhanced modes volumetric and shear locking free behaviour of the original formulation and does not exhibit hour‐glassing for large deformations.
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Based on the recent advances of hybrid stress finite elements, a seriesof alternative stress assumptions for these elements are investigated.Several new element models are…
Abstract
Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.