Benchmark tests for verifying discrete element modelling codes at particle impact level

Over the past 30 years, the Discrete Element Method (DEM) has rapidly gained popularity as a tool for modelling the behaviour of granular assemblies and is being used extensively in both scientific and industrial applications. However, it is far from clear from reviewing the literature whether the large number of DEM codes have been verified and checked against fundamental benchmark problems. DEM simulates the dynamics of each particle in an assembly by calculating the acceleration resulting from all the contact forces and body forces. It is clearly necessary that such a model be validated or verified by comparing with experimental results, analytical solutions or other numerical results (e.g. Finite Element Analysis (FEA) results) at particle impact level. There appears to be no standard benchmark tests against which DEM codes can be verified. It is thus essential and useful to establish a set of standard benchmark tests to confirm that these DEM codes are modelling the particle dynamics as intended. This paper proposes a set of benchmark tests to verify DEM codes at particle impact level for spherical particles. The analytical solutions derived from elasticity theory for elastic normal collision of two spheres or a sphere with a rigid plane are first reviewed. These analytical solutions apply only to the elastic regime for normal impact. Secondly, the analytical solutions of frictional oblique impact between two spheres or a sphere with a rigid plane are scrutinized and derived. These analytical solutions originate from the dynamics principles and should be satisfied for any DEM contact force model with prescribed friction and restitution coefficients. A set of eight benchmark tests are designed and performed using commercial DEM codes. Test 1 and Test 2 consider the elastic normal impact of two spheres or a sphere with a rigid plane, whereas the other tests (Test 3–Test 8) investigate the energy dissipation due to the collision. These benchmark tests also involve different types of material. The DEM results were compared with the analytical solutions, experimental or FEA results found in the literature. All benchmark tests showed good to excellent match, providing a quantitative verification for the codes used in this study. These benchmark tests not only verify DEM codes but also enhance the understanding of fundamental impact phenomena for modelling a large number of particles.     

Chaste: using agile programming techniques to develop computational biology software

Cardiac modelling is the area of physiome modelling where the available simulation software is perhaps most mature, and it therefore provides an excellent starting point for considering the software requirements for the wider physiome community. In this paper, we will begin by introducing some of the most advanced existing software packages for simulating cardiac electrical activity. We consider the software development methods used in producing codes of this type, and discuss their use of numerical algorithms, relative computational efficiency, usability, robustness and extensibility. We then go on to describe a class of software development methodologies known as test-driven agile methods and argue that such methods are more suitable for scientific software development than the traditional academic approaches. A case study is a project of our own, Cancer, Heart and Soft Tissue Environment, which is a library of computational biology software that began as an experiment in the use of agile programming methods. We present our experiences with a review of our progress thus far, focusing on the advantages and disadvantages of this new approach compared with the development methods used in some existing packages. We conclude by considering whether the likely wider needs of the cardiac modelling community are currently being met and suggest that, in order to respond effectively to changing requirements, it is essential that these codes should be more malleable. Such codes will allow for reliable extensions to include both detailed mathematical models--of the heart and other organs--and more efficient numerical techniques that are currently being developed by many research groups worldwide.     

An object‐oriented programming approach to the Lagrangian FEM analysis of large inelastic deformations and metal‐forming processes

The general deformation problem with material and geometric non‐linearities is typically divided into a number of subproblems including the kinematic, the constitutive, and the contact/friction subproblems. These problems are introduced for algorithmic purposes; however, each of them represents distinct physical aspects of the deformation process. For each of these subproblems, several well‐established mathematical and numerical models based on the finite element method have been proposed for their solution. Recent developments in software engineering and in the field of object‐oriented C++ programming have made it possible to model physical processes and mechanisms more expressively than ever before. In particular, the various subproblems and computational models in a large inelastic deformation analysis can be implemented using appropriate hierarchies of classes that accurately represent their underlying physical, mathematical and/or geometric structures. This paper addresses such issues and demonstrates that an approach to deformation processing using classes, inheritance and virtual functions allows a very fast and robust implementation and testing of various physical processes and computational algorithms. Here, specific ideas are provided for the development of an object‐oriented C++ programming approach to the FEM analysis of large inelastic deformations. It is shown that the maintainability, generality, expandability, and code re‐usability of such FEM codes are highly improved. Finally, the efficiency and accuracy of an object‐oriented programming approach to the analysis of large inelastic deformations are investigated using a number of benchmark metal‐forming examples. Copyright © 1999 John Wiley & Sons, Ltd.     

基于计算接触力学的粗颗粒土体材料细观性质模拟

采用离散元等数值模拟方法研究粗颗粒土体材料的细观力学行为,是近年来岩土力学的热点研究课题。提出了一种基于计算接触力学的粗颗粒土体材料细观力学行为模拟分析新方法。该法将土体颗粒剖分成一定数量的单元,通过计算接触力学方法模拟颗粒间的多体接触行为,是一种基于有限元变分原理的隐式数值求解方法,具有严格的理论基础。和离散元法方法相比,该方法在描述颗粒本身的力学特性方面具有优势,可以计算得到颗粒内部的应力分布情况,从而为颗粒破碎等细观行为的模拟计算提供依据。利用所发展的粗颗粒土体多体接触有限元计算程序,进行了不同围压的常规三轴数值试验,模拟计算结果符合粗颗粒土体材料三轴试验的一般规律,初步验证了所提出的计算方法的适用性。     

Computational modeling of cardiac electrophysiology: A novel finite element approach

The key objective of this work is the design of an unconditionally stable, robust, efficient, modular, and easily expandable finite element‐based simulation tool for cardiac electrophysiology. In contrast to existing formulations, we propose a global–local split of the system of equations in which the global variable is the fast action potential that is introduced as a nodal degree of freedom, whereas the local variable is the slow recovery variable introduced as an internal variable on the integration point level. Cell‐specific excitation characteristics are thus strictly local and only affect the constitutive level. We illustrate the modular character of the model in terms of the FitzHugh–Nagumo model for oscillatory pacemaker cells and the Aliev–Panfilov model for non‐oscillatory ventricular muscle cells. We apply an implicit Euler backward finite difference scheme for the temporal discretization and a finite element scheme for the spatial discretization. The resulting non‐linear system of equations is solved with an incremental iterative Newton–Raphson solution procedure. Since this framework only introduces one single scalar‐valued variable on the node level, it is extremely efficient, remarkably stable, and highly robust. The features of the general framework will be demonstrated by selected benchmark problems for cardiac physiology and a two‐dimensional patient‐specific cardiac excitation problem. Copyright © 2009 John Wiley & Sons, Ltd.     

Large-scale grid-enabled lattice Boltzmann simulations of complex fluid flow in porous media and under shear

Well-designed lattice Boltzmann codes exploit the essentially embarrassingly parallel features of the algorithm and so can be run with considerable efficiency on modern supercomputers. Such scalable codes permit us to simulate the behaviour of increasingly large quantities of complex condensed matter systems. In the present paper, we present some preliminary results on the large-scale three-dimensional lattice Boltzmann simulation of binary immiscible fluid flows through a porous medium, derived from digitized X-ray micro-tomographic data of Bentheimer sandstone, and from the study of the same fluids under shear. Simulations on such scales can benefit considerably from the use of computational steering, and we describe our implementation of steering within the lattice Boltzmann code, called LB3D, making use of the RealityGrid steering library. Our large-scale simulations benefit from the new concept of capability computing, designed to prioritize the execution of big jobs on major supercomputing resources. The advent of persistent computational grids promises to provide an optimal environment in which to deploy these mesoscale simulation methods, which can exploit the distributed nature of computer, visualization and storage resources to reach scientific results rapidly; we discuss our work on the grid-enablement of lattice Boltzmann methods in this context.     

草帽型大跨空间结构的风压数值模拟与关键参数影响分析

基于计算流体动力学（CFD）和SST k-ε湍流模型,运用FLUENT软件针对草帽型大跨空间结构表面风压及其规律进行数值模拟和分析比较,运用典型算例分析对比模拟结果与既有文献结果,以验证数值模拟的可信性。系统性研究了结构高跨比等关键参数对草帽型空间结构表面不同部位风压分布的影响。     

Scheduling multistage hybrid flowshops with multiprocessor tasks by an effective heuristic

This study considers the scheduling problem of multistage hybrid flowshops with multiprocessor tasks, which is a core topic for numerous industrial applications. An effective and efficient heuristic, namely the heuristic of multistage hybrid flowshops (HMHF) is proposed to solve this problem. To verify the developed heuristic, computational experiments are conducted on a well-known benchmark problem set. The results are compared with 10 constructive heuristics and a tabu search (TS) based meta-heuristic from the relevant literature. These computational results show that the proposed HMHF heuristic is highly effective when compared to these algorithms for this problem on the same benchmark instances.     

Balancing of U-type assembly systems using simulated annealing

The paper presents a new simulated annealing (SA)-based algorithm for the assembly line-balancing problem with a U-type configuration. The proposed algorithm employs an intelligent mechanism to search a large solution space. U-type assembly systems are becoming increasingly popular in today's modern production environments since they are more general than the traditional assembly systems. In these systems, tasks are to be allocated into stations by moving forward and backward through the precedence diagram in contrast to a typical forward move in the traditional assembly systems. The performance of the algorithm is measured by solving a large number of benchmark problems available in the literature. The results of the computational experiments indicate that the proposed SA-based algorithm performs quite effectively. It also yields the optimal solution for most problem instances. Future research directions and a comprehensive bibliography are also provided here.     

Applying a hybrid simulated annealing and tabu search approach to non-permutation flowshop scheduling problems

Researchers have indicated that a permutation schedule can be improved by a non-permutation schedule in a flowshop with completion time-based criteria, such as makespan and total completion time. This study proposes a hybrid approach which draws on the advantages of simulated annealing and tabu search for the non-permutation flowshop scheduling problem, in which the objective function is the makespan of the schedule. To verify the effectiveness of the proposed hybrid approach, computational experiments are performed on a set of well-known non-permutation flowshop scheduling benchmark problems. The result shows that the performance of the hybrid approach is better than that of other approaches, including ant colony optimisation, simulated annealing, and tabu search. Further, the proposed approach found new upper bound values for all benchmark problems within a reasonable computational time.     

Computational modeling of muscular thin films for cardiac repair

Motivated by recent success in growing biohybrid material from engineered tissues on synthetic polymer films, we derive a computational simulation tool for muscular thin films in cardiac repair. In this model, the polydimethylsiloxane base layer is simulated in terms of microscopically motivated tetrahedral elements. Their behavior is characterized through a volumetric contribution and a chain contribution that explicitly accounts for the polymeric microstructure of networks of long chain molecules. Neonatal rat ventricular cardiomyocytes cultured on these polymeric films are modeled with actively contracting truss elements located on top of the sheet. The force stretch response of these trusses is motivated by the cardiomyocyte force generated during active contraction as suggested by the filament sliding theory. In contrast to existing phenomenological models, all material parameters of this novel model have a clear biophyisical interpretation. The predictive features of the model will be demonstrated through the simulation of muscular thin films. First, the set of parameters will be fitted for one particular experiment documented in the literature. This parameter set is then used to validate the model for various different experiments. Last, we give an outlook of how the proposed simulation tool could be used to virtually predict the response of multi-layered muscular thin films. These three-dimensional constructs show a tremendous regenerative potential in repair of damaged cardiac tissue. The ability to understand, tune and optimize their structural response is thus of great interest in cardiovascular tissue engineering.     

Monte Carlo simulation of the movement and detection efficiency of a whole-body counting system using a BOMAB phantom

This study reports on the computational analysis and experimental calibration of the whole-body counting detection equipment at the Nuclear and Technological Institute (ITN) in Portugal. Two state-of-the-art Monte Carlo simulation programmes were used for this purpose: PENELOPE and MCNPX. This computational work was undertaken as part of a new set of experimental calibrations, which improved the quality standards of this study's WBC system. In these calibrations, a BOMAB phantom, one of the industry standards phantoms for WBC calibrations in internal dosimetry applications, was used. Both the BOMAB phantom and the detection system were accurately implemented in the Monte Carlo codes. The whole-body counter at ITN possesses a moving detector system, which poses a challenge for Monte Carlo simulations, as most codes only accept static configurations. The continuous detector movement was approximately described in the simulations by averaging several discrete positions of the detector throughout the movement. The computational efficiency values obtained with the two Monte Carlos codes have deviations of less than 3.2 %, and the obtained deviations between experimental and computational efficiencies are less than 5 %. This work contributes to demonstrate the great effectiveness of using computational tools for understanding the calibration of radiation detection systems used for in vivo monitoring.     

COMPUTATIONAL ASPECTS OF GEOMETRIC PROGRAMMING 2. POLYNOMIAL PROGRAMMING

An attempt is made to examine the computational aspects of Geometric Programming within a systematic framework. The many numerical algorithms, which have been proposed, and used extensively on practical optimization problems, are considered in relation to developments in general Nonlinear Programming. An effort is made to provide explanations for some of the computational results reported in the literature for specific Polynomial Programming codes and general conclusions on the question of computational efficiency are drawn. The restricted case of “Posynomial“ Programming is considered in detail first, since it forms the core of algorithms used to solve the general Signomial case, which is dealt with subsequently.     

Model-based simulation of the synergistic effects of blast and fragmentation on a concrete wall using the MPM

With the development of the material point method (MPM) that is an extension from computational fluid dynamics (CFD) to computational structural dynamics (CSD), a model-based simulation is performed in this paper to investigate the synergistic effects of blast and fragmentation on structural failure. As can be found from the open literature, the synergistic effects of blast and fragmentation have been usually simulated via a combined approach through an interface between CFD codes and CSD codes. As a consequence, numerical solutions are very sensitive to the choices of different time steps and spatial meshes for different physical phenomena, especially for the multi-physics involved in the initiation and evolution of structural failure. Hence, a coupled approach within a single computational domain seems to be necessary if objective results are needed. In this paper, a numerical procedure is proposed with the use of the MPM, so that different kinds of gradient and divergence operators could be discretized in a single computational domain without involving fixed mesh connectivity. To simulate the evolution of impact failure, the transition from continuous to discontinuous failure modes is identified via the bifurcation analysis. The potential of the proposed model-based simulation procedure is demonstrated through 1D and 2D isothermal cases including cased bomb expansion and fragmentation, blast wave expansion through a broken case, and blast and fragment impact on a concrete wall. The preliminary results obtained in this numerical study provide a better understanding of the synergistic effects on impact/blast-resistant structural design. An integrated experimental, analytical and computational effort is required to further improve the proposed procedure for general applications.     

A reacting shock in a spherically symmetric gas

A two-phase Stefan problem with latent heat a general power function of position is investigated. The background of the problem can be found in the soil-freezing process during the application of the artificial ground-freezing technique. After introducing the specific engineering condition, the governing equations of a two-phase Stefan problem are developed. An exact solution for the problem is established using the similarity transformation technique and the theory of the Kummer functions. It is proved that the coefficients in the solution can be appropriately determined if certain inequality is satisfied. Special cases of the solution are discussed, and several solutions reported in the literature are recovered. A similar two-phase Stefan problem involving first type of boundary condition is also introduced and solved. The coefficients in the solution can always be properly determined with no additional requirement. In the end, computational examples of the solution are presented and discussed. The exact solution provides a useful benchmark that can be used for verifying general numerical algorithms of Stefan problems, and it is also advantageous in the context of the inverse problem analysis.     

Mixed Arlequin method for multiscale poromechanics problems

An Arlequin poromechanics model is introduced to simulate the hydro‐mechanical coupling effects of fluid‐infiltrated porous media across different spatial scales within a concurrent computational framework. A two‐field poromechanics problem is first recast as the twofold saddle point of an incremental energy functional. We then introduce Lagrange multipliers and compatibility energy functionals to enforce the weak compatibility of hydro‐mechanical responses in the overlapped domain. To examine the numerical stability of this hydro‐mechanical Arlequin model, we derive a necessary condition for stability, the twofold inf–sup condition for multi‐field problems, and establish a modified inf–sup test formulated in the product space of the solution field. We verify the implementation of the Arlequin poromechanics model through benchmark problems covering the entire range of drainage conditions. Through these numerical examples, we demonstrate the performance, robustness, and numerical stability of the Arlequin poromechanics model. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical prediction of damage in composite structures from soft body impacts

The paper summarises recent progress on materials modelling and numerical simulation of soft body impact damage in fibre reinforced composite aircraft structures. The work is based on the application of finite element (FE) analysis codes to simulate damage in composite shell structures under impact loads. Composites ply damage models and interply delamination models have been developed and implemented in commercial explicit FE codes. Models are discussed for predicting impact loads on aircraft structures arising from deformable soft bodies such as gelatine (synthetic bird) and ice (hailstone). The composites failure models and code developments are briefly summarised and applied in the paper to numerical simulation of synthetic bird impact on idealised composite aircraft structures.     

Monte Carlo and variance reduction methods for structural reliability analysis: A comprehensive review

Monte Carlo methods have attracted constant and even increasing attention in structural reliability analysis with a wide variety of developments seamlessly presented over decades. Along the way, a number of specialized reviews and benchmark studies have been provided from time to time, aiming at summarizing and comparing selected few approaches in detail, mainly from an implementation point of view. In contrast, the aim of the present survey is to play a comprehensive role as a methodological guidebook on Monte Carlo simulation and its related, especially variance reduction, techniques through a covering of 444 references in the relevant literature. To achieve this goal, we present an extensive review of formulations and techniques along with insightful summaries of developments of existing numerical methods, ranging from the general formulation, sub-categories and variants, to their combined uses with other simulation techniques and surrogate models, as well as the key advantages and assumptions.