Multi-physics-multi-scale simulation and optimisation: the next generation

FEA and CFD analysis is becoming ever more complex with an emerging demand for simulation software technologies that can address ranges of problems that involve combinations of interactions amongst varying physical phenomena over a variety of time and length scales. Computation modelling of such problems requires software technologies that enable the representation of these complex suites of 'physical' interactions. This functionality requires the structuring of simulation modules for specific physical phemonmena so that the coupling can be effectiely represented. These 'multi-physics' and 'multi-scale' computations are very compute intensive and so the simulation software must operate effectively in parallel if it is to be used in this context. Of course the objective of 'multi-physics' and 'multi-scale' simulation is the optimal design of engineered systems so optimistation is an important feature of such classes of simulation. In this presentation, a multi-disciplinary approach to simulation based optimisation is described with some key examples of application to challenging engineering problems.

Simulation de profils de gravure et de dépôt à l’échelle du motif pour l’étude des procédés de microfabrication utilisant une source plasma de haute densité à basse pression

En lien avec l’avancée rapide de la réduction de la taille des motifs en microfabrication, des processus physiques négligeables à plus grande échelle deviennent dominants lorsque cette taille s’approche de l’échelle nanométrique. L’identification et une meilleure compréhension de ces différents processus sont essentielles pour améliorer le contrôle des procédés et poursuivre la «nanométrisation» des composantes électroniques. Un simulateur cellulaire à l’échelle du motif en deux dimensions s’appuyant sur les méthodes Monte-Carlo a été développé pour étudier l’évolution du profil lors de procédés de microfabrication. Le domaine de gravure est discrétisé en cellules carrées représentant la géométrie initiale du système masque-substrat. On insère les particules neutres et ioniques à l’interface du domaine de simulation en prenant compte des fonctions de distribution en énergie et en angle respectives de chacune des espèces. Le transport des particules est effectué jusqu’à la surface en tenant compte des probabilités de réflexion des ions énergétiques sur les parois ou de la réémission des particules neutres. Le modèle d’interaction particule-surface tient compte des différents mécanismes de gravure sèche telle que la pulvérisation, la gravure chimique réactive et la gravure réactive ionique. Le transport des produits de gravure est pris en compte ainsi que le dépôt menant à la croissance d’une couche mince. La validité du simulateur est vérifiée par comparaison entre les profils simulés et les observations expérimentales issues de la gravure par pulvérisation du platine par une source de plasma d’argon.

Enabling industrial scale simulation / emulation models

OLE Process Control (OPC) is an industry standard that facilitates the communication between PCs and Programmable Logic Controllers (PLC). This communication allows for the testing of control systems with an emulation model. When models require faster and higher volume communications, limitations within OPC prevent this. In this paper an interface is developed to allow high speed and high volume communications between a PC and PLC enabling the emulation of larger and more complex control systems and their models. By switching control of elements within the model between the model engine and the control system it is possible to use the model to validate the system design, test the real world control systems and visualise real world operation.

Atomic scale simulation of deformation in magnesium single crystals

The deformation behaviour of magnesium single crystals under plane strain conditions has been examined using molecular dynamics modelling. The simulations were based on an existing atomic potential for magnesium taken from the literature. A strain of 10% was applied at rates of 3x10⁹s^-1 and 3x10⁷s^-1. The simulations predicted the formation of mechanical twins that accommodated extension in the c-axis direction of the hexagonal unit cell. However, the predicted twin is not of the same kind found in magnesium, but is that commonly observed in titanium. It is believed that further analysis of the physical properties predicted by this interatomic potential will shed more light on the atomic processes controlling twinning in Magnesium alloys. It also highlights the need for improvements to the interatomic potential such that more accurate deformation behaviour can be attained.

Multi-scale simulation using a hybrid mass-spring system and finite element model

Ply-scale finite element (FE) models are widely used to predict the performance of a composite structure based on material properties of individual plies. When simulating damage, these models neglect microscopic fracture processes which may have a significant effect on how a crack progresses within and between plies of a multidirectional laminate. To overcome this resolution limitation a multi-scale modelling technique is employed to simulate the effect micro-scale damage events have on the macro-scale response of a structure. The current paper discusses the development and validation of a hybrid mass-spring system and finite element modelling technique for multi-scale analysis. The model developed here is limited to elastic deformations; however, it is the first key step towards an efficient multi-scale damage model well suited to simulation of fracture in fibre reinforced composite materials. Various load cases have been simulated using the model developed here which show excellent accuracy compared to analytical and FE results. Future work is discussed, including extension of the model to incorporate damage modelling.

2-D R-matrix propagation: A large scale electron scattering simulation dominated by the multiplication of dynamically changing matrices

We examine the computational aspects of propagating a global R-matrix, R, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of R, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper.

simulation and interaction of fluid dynamics

In the fluid simulation, the fluids and their surroundings may greatly change properties such as shape and temperature simultaneously, and different surroundings would characterize different interactions, which would change the shape and motion of the fluids in different ways. On the other hand, interactions among fluid mixtures of different kinds would generate more comprehensive behavior. To investigate the interaction behavior in physically based simulation of fluids, it is of importance to build physically correct models to represent the varying interactions between fluids and the environments, as well as interactions among the mixtures. In this paper, we will make a simple review of the interactions, and focus on those most interesting to us, and model them with various physical solutions. In particular, more detail will be given on the simulation of miscible and immiscible binary mixtures. In some of the methods, it is advantageous to be taken with the graphics processing unit (GPU) to achieve real-time computation for middle-scale simulation.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

Atomic ordering in nano-layered FePt: Multiscale Monte Carlo simulation

Nano- and meso-scale simulation of chemical ordering kinetics in nano-layered L1(0)-AB binary intermetallics was performed. In the nano- (atomistic) scale Monte Carlo (MC) technique with vacancy mechanism of atomic migration implemented with diverse models for the system energetics was used. The meso-scale microstructure evolution was, in turn, simulated by means of a MC procedure applied to a system built of meso-scale voxels ordered in particular L1(0) variants. The voxels were free to change the L1(0) variant and interacted with antiphase-boundary energies evaluated within the nano-scale simulations. The study addressed FePt thin layers considered as a material for ultra-high-density magnetic storage media and revealed metastability of the L1(0) c-variant superstructure with monoatomic planes parallel to the (001)-oriented layer surface and off-plane easy magnetization. The layers, originally perfectly ordered in the c-variant, showed discontinuous precipitation of a- and b-L1(0)-variant domains running in parallel with homogeneous disordering (i.e. generation of antisite defects). The domains nucleated heterogeneously on the free monoatomic Fe surface of the layer, grew inwards its volume and relaxed towards an equilibrium microstructure of the system. Two

Molecular dynamics simulation (MDS) to study nanoscale machining processes

Molecular Dynamics Simulations (MDS) are constantly being used to make important contributions to our fundamental understanding of material behaviour, at the atomic scale, for a variety of thermodynamic processes. This chapter shows that molecular dynamics simulation is a robust numerical analysis tool in addressing a range of complex nanofinishing (machining) problems that are otherwise difficult or impossible to understand using other methods. For example the mechanism of nanometric cutting of silicon carbide is influenced by a number of variables such as machine tool performance, machining conditions, material properties, and cutting tool performance (material microstructure and physical geometry of the contact) and all these variables cannot be monitored online through experimental examination. However, these could suitably be studied using an advanced simulation based approach such as MDS. This chapter details how MD simulation can be used as a research and commercial tool to understand key issues of ultra precision manufacturing research problems and a specific case was addressed by studying diamond machining of silicon carbide. While this is appreciable, there are a lot of challenges and opportunities in this fertile area. For example, the world of MD simulations is dependent on present day computers and the accuracy and reliability of potential energy functions [109]. This presents a limitation: Real-world scale simulation models are yet to be developed. The simulated length and timescales are far shorter than the experimental ones which couples further with the fact that contact loading simulations are typically done in the speed range of a few hundreds of m/sec against the experimental speed of typically about 1 m/sec [17]. Consequently, MD simulations suffer from the spurious effects of high cutting speeds and the accuracy of the simulation results has yet to be fully explored. The development of user-friendly software could help facilitate molecular dynamics as an integral part of computer-aided design and manufacturing to tackle a range of machining problems from all perspectives, including materials science (phase of the material formed due to the sub-surface deformation layer), electronics and optics (properties of the finished machined surface due to the metallurgical transformation in comparison to the bulk material), and mechanical engineering (extent of residual stresses in the machined component) [110]. Overall, this chapter provided key information concerning diamond machining of SiC which is classed as hard, brittle material. From the analysis presented in the earlier sections, MD simulation has helped in understanding the effects of crystal anisotropy in nanometric cutting of 3C-SiC by revealing the atomic-level deformation mechanisms for different crystal orientations and cutting directions. In addition to this, the MD simulation revealed that the material removal mechanism on the (111) surface of 3C-SiC (akin to diamond) is dominated by cleavage. These understandings led to the development of a new approach named the “surface defect machining” method which has the potential to be more effective to implement than ductile mode micro laser assisted machining or conventional nanometric cutting.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.