Progressive collapse analysis of precast frame structures based on discrete element method

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

A new discrete element-embedded finite element method for transient deformation, movement and heat transfer in packed bed

In this work, we review three kinds of numerical algorithms, namely the discrete element method (DEM), the coupling discrete element and finite element method (DEM/FEM) and the cohesive zone model (CZM), for the impact fracture simulations of automotive laminated glass. Based on the non-continuum theory, the DEM is capable of modeling the impact fracture phenomenon. However, this method is very time-consuming. To remedy this shortcoming, we have been devoted to combining the discrete element method and the finite element method. Another notable work is to simulate the impact fracture behaviors by using the CZM. Some future works concerning this research aspect are also presented.

Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures or (ii) modeling the rock by a discrete (or discontinuous) approach that describes the material directly as a collection of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified so that they reproduce the discretization of a first-order finite element method (FEM) for linear elasticity. This provides an expression of the virtual forces in terms of general Hook’s macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in a reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it enables a direct coupling between (M)DEM and domains modeled by a grid made of polyhedral cells. Thus, this approach makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate the simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented using the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work provides a more uniform approach and extends these previous works to general polyhedral grids for the non-fracturing domain.

In discrete element methods the simulated bodies are typically assumed to be infinitely rigid in order to reduce the computational cost. However, there are multibody systems where it is useful to take into account the deformability of the simulated bodies in order to enable the evaluation of their stress and strain distributions. This paper focuses on the simulation of systems of multiple deformable bodies using a combination of discrete and finite element methods (FEM), with some simplifying assumptions that are necessary to make the solution of the problem feasible. In traditional mixed FE formulations the contact effects can be taken into account using Lagrange multipliers methods and keeping the contact surfaces and forces as unknowns together with the unknown displacements. This approach results in huge systems of highly nonlinear coupled equations due to geometric as well as boundary nonlinearities. Furthermore, the parts of the bodies that may come in contact, typically, have to be identified before performing the simulation. However, no prior knowledge of the upcoming contacts is available in the multibody systems under consideration. Considering the excessive computational requirements, due to the huge number of degrees-of-freedom (DOF) and the high nonlinearities of the coupled systems of equations, it is unrealistic to solve problems involving many interacting bodies using such classical contact FE approaches. Simulations of deformable bodies with reasonable computational cost are enabled by incorporating FEM in DE analyses using certain assumptions that uncouple the contact interactions from the equations of dynamic equilibrium. In particular, the DEM are employed to identify, at each simulation step, the bodies in contact and determine the contact forces. Then, either a FE or a DE formulation is used at the individual body level to describe the equations of motion, depending whether the body under consideration is deformable or rigid, respectively. In case of a deformable body, the strains are assumed to be sufficiently small to permit a small strains, although large displacements, analysis. The deformability of individual bodies is taken into account using a displacement-based (DB) Updated-Lagrangian (UL) Finite Element (FE) formulation. Finally, an explicit time integration method, specifically the central difference method (CDM), is used to perform the numerical direct integration of the equations of motion and determine the new displacements, as well as the deformations and stresses wherever needed, of each body. Having computed the motion of each discrete body at a new time step, the positions of all discrete bodies are updated and a new contact detection process determines the new contacts and evaluates the corresponding contact forces, which are then used in the following time step.

Scaled-up rice grain modelling for DEM calibration and the validation of hopper flow

This paper carries out a survey on available methods for micromechanical modelling on asphalt mixture. Focus is placed on models based on different concepts as well as different computational methods in numerical implementation. The major topics covered include: models based on discrete element method, micromechanical finite element models, disturbed state concept, the discontinuous deformation analysis method, integration of mechanics on different scales, etc. A brief description of some fundamental algorithms in discrete element and finite element methods are also included due to the modelling accuracy and thus wide interest in them. Simple case studies are included to illustrate the methods in discussion wherever space allows.

This document explores the possibility of the discrete element method (DEM) being applied in nonlinear dynamic analysis of space frame structures. The method models the analyzed object to be composed by finite particles and the Newton’s second law is applied to describe each particle’s motion. The parallel-bond model is adopted during the calculation of internal force and moment arising from the deformation. The procedure of analysis is vastly simple, accurate and versatile. Numerical examples are given to demonstrate the accuracy and applicability of this method in handling the large deflection and dynamic behaviour of space frame structures. Besides, the method does not need to form stiffness matrix or iterations, so it is more advantageous than traditional nonlinear finite element method.

A discrete element method (DEM) has widely been used to simulate asphalt mixture characteristics, and DEM models can consider the effect of aggregate gradation and interaction between particles. However, proper selection of model parameters is crucial to obtain convincing results from DEM‐based simulations. This paper presents a method to appropriately determine the mechanical parameters to be used in DEM‐based simulation of asphalt concrete mixture. Splitting test specimens are prepared by using asphalt mixture, and the splitting test results are compared with simulation results from two‐dimensional (2D) DEM and three‐dimensional (3D) DEM. Basing on the DEM results, the effects of contact model parameters on the simulation results are analyzed. The slope of the load‐displacement curve at the beginning stage is mainly affected by the stiffness parameters, and the peak load is mainly determined by using the value of the bond strength. The laboratory splitting test of AC‐20 and AC‐13 specimens were performed at different temperatures, namely, −10°C, 0°C, 10°C, and 20°C, and the load‐displacement relationships were plotted. According to the real load‐displacement curve’s slope at the beginning stage and peak load applied, the range of DEM bond model parameters is determined. On the basis of DEM results of the splitting test, the relationships between simulation load‐displacement curve’s characteristics and bond model parameters are fitted. The values of the parameters of the DEM contact bond model at different temperatures are obtained depending on the actual load‐displacement curve’s initial slope and peak load. Lastly the DEM and laboratory test results are compared, which illustrates that the parallel bond model can well simulate the behavior of asphalt mixture.

Simulation of fracturing processes in porous rocks can be divided in two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or discontinuous) modeling technique that describes the material directly as an assembly of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified in all regions without failing elements so that they reproduce the discretization of linear FEM for linear elasticity. This provides an expression of the virtual forces in terms of general Hook's macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of traditional FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it gives the basis for coupling (M)DEM to domains with linear elasticity described by polyhedral grids, which makes it easier to apply realistic boundary conditions in hydraulic-fracturing simulations. This approach also makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented in the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work is a more uniform approach and extends previous work to general polyhedral grids for the non-fracturing domain.

A co-rotational curved beam element for geometrically nonlinear analysis of framed structures

The discrete element method (DEM) is ideal for modeling many problems not accessible to traditional continuum-based methods such as finite difference and finite elements. DEM has the advantage of inherently capturing large non-affine deformations and the fluid—solid phase changes so commonly found in granular media. The DEM appears to derive much of its power from the kinematic freedom for the particles such that seemingly simplistic micro-scale models can replicate realistic macro-scale behavior. With the advent of large-scale computing, by which simulations of several million particles are possible, the DEM will become an important tool for geotechnical and industrial applications within the next 20 years. The advances in DEM have and will continue to mirror advances in computer hardware. Several advances in DEM technology will accompany the improvements in computer technology. The constitutive response of the DEM medium depends on micro-scale laws that define the contact mechanisms, particle size and shape, and particle distribution. The success of the method requires a correlation between the phenomenology of the DEM medium and the micro-scale laws. Most of these advances will be accomplished through numerical experiments, which at present are a popular tool for understanding granular media as a continuum. Is it reasonable to foresee a day when a continuum view is unnecessary? In this paper, this question is discussed from the standpoint of scale effects that infect all numerical approximations, whether the governing equations are derived from a continuum relationship or begin from a discrete model. The key point is that unless computing power reaches a point where there is a one-to-one correspondence between simulated particle size and actual particle size, some understanding of the DEM medium as a continuum will be needed.

Numerical modeling methods, such as the discrete element method (DEM), are an increasingly popular alternative to traditional semi-empirical terramechanics techniques. While DEM has many advantages, including the ability to model more complex running gear and terrain profiles, it has not reached widespread popularity due to its high computation costs. In this study a surrogate DEM model (S-DEM) was developed to maintain the simulation accuracy and capabilities of DEM with reduced computation costs. This marks one of the first surrogate models developed for DEM, and the first known model developed for terramechanics. By storing wheel-soil interaction forces and soil velocities extracted from constant-velocity DEM simulations, S-DEM can quickly perform new dynamic wheel locomotion simulations. Using both DEM and S-DEM, wheel locomotion simulations were performed on flat and rough terrain. S-DEM was found to reproduce drawbar pull and driving torque well in both cases, though wheel sinkage errors were significant at times. Computation costs were reduced by three orders of magnitude in comparison to DEM, bringing the benefits of DEM modeling to vehicle design and control. The techniques used to develop S-DEM may be applicable to other common DEM applications, such as soil drilling, excavating, and plowing.

A practical multiscale modeling strategy to model wet-type beam–column connections for seismic analysis of precast RC frame structures

For Beams and columns in the nonlinear analysis of structures concerned with earthquake ground motions, member restoring-force model is one of the important aspects for adequate evaluation of structural numerical analyses. The Member Endochronic Model (MEM) is a kind of new restoring-force model for beams and columns. Studies on MEM under compound forces and reversal forces are still going on and some improvements have tried to develop its feasibility. MEM is established on the combined idea of section endochronic description and the member model of the finite element method. The most important feature of MEM is that the section characteristics under compound and reversal forces are described on the concept of section intrinsic time, which makes the section constitutive equation being uniform for monotonic loading or reversal loading and for one-dimensional deformation or compound forces case. This could greatly simplify the computer programming work of structure analysis. After a brief introduction on the establishment of MEM and the method for determining the model parameters, this paper puts the model into the inelastic analysis of plane steel frames to examine the applicability of the model on the simulation analysis of frame structures. The numerical results are represented by a series of section quantities of the member ends including the section intrinsic time. The consequences of the plastic hinge appearance of each member are especially examined to show the adequate description of the model on the frame damage course. The ductility indices of plastic hinges of member ends and the whole structure are also examined. It is shown that MEM is reliable on the push-over analysis of frame structures and the special section description based on the section intrinsic time is convenient for the understanding for the damage state of the structure. Results of the paper show the possibility for the further use of MEM to structural dynamic analysis.