Modelling of industrial multi-physics processes—a key role for computational mechanics.

In the analysis of industrial processes, there is an increasing emphasis on systems governed by interacting continuum phenomena. Mathematical models of such multi-physics processes can only be achieved for practical simulations through computational solution procedures—computational mechanics. Examples of such multi-physics systems in the context of metals processing are used to explore some of the key issues. Finite-volume methods on unstructured meshes are proposed as a means to achieve efficient rapid solutions to such systems. Issues associated with the software design, the exploitation of high performance computers, and the concept of the virtual computational-mechanics modelling laboratory are also addressed in this context.

CAPLib - A 'thin layer' message passing library to support computational mechanics codes on distributed memory parallel systems

The Computer Aided Parallelisation Tools (CAPTools) [Ierotheou, C, Johnson SP, Cross M, Leggett PF, Computer aided parallelisation tools (CAPTools)-conceptual overview and performance on the parallelisation of structured mesh codes, Parallel Computing, 1996;22:163±195] is a set of interactive tools aimed to provide automatic parallelisation of serial FORTRAN Computational Mechanics (CM) programs. CAPTools analyses the user's serial code and then through stages of array partitioning, mask and communication calculation, generates parallel SPMD (Single Program Multiple Data) messages passing FORTRAN. The parallel code generated by CAPTools contains calls to a collection of routines that form the CAPTools communications Library (CAPLib). The library provides a portable layer and user friendly abstraction over the underlying parallel environment. CAPLib contains optimised message passing routines for data exchange between parallel processes and other utility routines for parallel execution control, initialisation and debugging. By compiling and linking with different implementations of the library, the user is able to run on many different parallel environments. Even with today's parallel systems the concept of a single version of a parallel application code is more of an aspiration than a reality. However for CM codes the data partitioning SPMD paradigm requires a relatively small set of message-passing communication calls. This set can be implemented as an intermediate `thin layer' library of message-passing calls that enables the parallel code (especially that generated automatically by a parallelisation tool such as CAPTools) to be as generic as possible. CAPLib is just such a `thin layer' message passing library that supports parallel CM codes, by mapping generic calls onto machine specific libraries (such as CRAY SHMEM) and portable general purpose libraries (such as PVM an MPI). This paper describe CAPLib together with its three perceived advantages over other routes: - as a high level abstraction, it is both easy to understand (especially when generated automatically by tools) and to implement by hand, for the CM community (who are not generally parallel computing specialists); - the one parallel version of the application code is truly generic and portable; - the parallel application can readily utilise whatever message passing libraries on a given machine yield optimum performance.

CFD approach for solid mechanics analysis

A cell-centred finite volume(CC-FV) solid mechanics formulation, based on a computational fluid dynamics(CFD) procedure, is presented. A CFD code is modified such that the velocity variable is used as to the displacement variable. Displacement and pressure fields are considered as unknown variables. The results are validated with finite element(FE) and cell-vertex finite volume(CV-FV) predictions based on discretisation of the equilibrium equations. The developed formulation is applicable for both compressible and incompressible solids behaviour. The method is general and can be extended for the simultaneous analysis of problems involving flow-thermal and stress effects.

Dynamic mesh partitioning and load-balancing for parallel computational mechanics codes

In this Chapter we discuss the load-balancing issues arising in parallel mesh based computational mechanics codes for which the processor loading changes during the run. We briefly touch on geometric repartitioning ideas and then focus on different ways of using a graph both to solve the load-balancing problem and the optimisation problem, both locally and globally. We also briefly discuss whether repartitioning is always valid. Sample illustrative results are presented and we conclude that repartitioning is an attractive option if the load changes are not too dramatic and that there is a certain trade-off between partition quality and volume of data that the underlying application needs to migrate.

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted.

Predicting the behaviour of micro-electronic displays using computational mechanics

Micro-electronic displays are indispensible devices used in high performance applications such as aerospace, medical, marine and industrial sectors.These devices provide an interface to real time mission critical devices and therefore require good optical visual performance and high reliability, all this within varied and challenging environments.

Fracture mechanics analysis of cracks in solder joint intermetallic compounds

The trend towards miniaturization of electronic products leads to the need for very small sized solder joints. Therefore, there is a higher reliability risk that too large a fraction of solder joints will transform into Intermetallic Compounds (IMCs) at the solder interface. In this paper, fracture mechanics study of the IMC layer for SnPb and Pb-free solder joints was carried out using finite element numerical computer modelling method. It is assumed that only one crack is present in the IMC layer. Linear Elastic Fracture Mechanics (LEFM) approach is used for parametric study of the Stress Intensity Factors (SIF, KI and KII), at the predefined crack in the IMC layer of solder butt joint tensile sample. Contrary to intuition, it is revealed that a thicker IMC layer in fact increases the reliability of solder joint for a cracked IMC. Value of KI and KII are found to decrease with the location of the crack further away from the solder interfaces while other parameters are constant. Solder thickness and strain rate were also found to have a significant influence on the SIF values. It has been found that soft solder matrix generates non-uniform plastic deformation across the solder-IMC interface near the crack tip that is responsible to obtain higher KI and KII.

Fracture Mechanics Analysis of the Dentine-Luting Cement Interface.

The objectives of this study were to determine the fracture toughness of adhesive interfaces between dentine and clinically relevant, thin layers of dental luting cements. Cements tested included a conventional glass-ionomer, F (Fuji I), a resin-modified glass-ionomer, FP (Fuji Plus) and a compomer cement, D (DyractCem). Ten miniature short-bar chevron notch specimens were manufactured for each cement, each comprising a 40 µm thick chevron of lute, between two 1.5 mm thick blocks of bovine dentine, encased in resin composite. The interfacial KIC results (MN/m3/2) were median (range): F; 0.152 (0.14-0.16), FP; 0.306 (0.27-0.37), D; 0.351 (0.31-0.37). Non-parametric statistical analysis showed that the fracture toughness of F was significantly lower (p

A micro-mechanics damage approach for fatigue of composite materials

A new model for fatigue damage evolution of polymer matrix composites (PMC) is presented. The model is based on a combination of an orthotropic damage model and an isotropic fatigue evolution model. The orthotropic damage model is used to predict the orthotropic damage evolution within a single cycle. The isotropic fatigue model is used to predict the magnitude of fatigue damage accumulated as a function of the number of cycles. This approach facilitates the determination of model parameters since the orthotropic damage model parameters can be determined from available data from quasi-static-loading tests. Then, limited amount of fatigue data is needed to adjust the fatigue evolution model. The combination of these two models provides a compromise between efficiency and accuracy. Decomposition of the state variables down to the constituent scale is accomplished by micro-mechanics. Phenomenological damage evolution models are then postulated for each constituent and for the micro-structural interaction among them. Model parameters are determined from available experimental data. Comparison between model predictions and additional experimental data is presented.

Fracture mechanics using a 3D composite element

The formulation of a 3D composite element and its use in a mixed-mode fracture mechanics example is presented. This element, like a conventional 3D finite element, has three degrees of freedom per node although, like a plate element, the strains are defined in the local directions of the mid-plane surface. The stress-strain property matrix of this element was modified to decouple the stresses in the local mid-plane and the strains normal to this plane thus preventing the element from being too stiff in bending. A main advantage of this formulation is the ability to model a laminate with a single 3D element. The motivation behind this work was to improve the computational efficiency associated with the calculation of strain energy release rates in laminated structures. A comparison of mixed-mode results using different elements of an in-house finite element package are presented. Good agreement was achieved between the results obtained using the new element and coventional higher-order elements

Progress in Fracture and Damage Mechanics

This special-topic volume reports on new progress made in the analysis and understanding of fracture and damage mechanics. The Finite Element Method is a well-established analytical tool for theoretical fracture analysis. The development of interface elements which combine aspects of both fracture and damage mechanics has permitted the prediction of both crack initiation and propagation. A number of the papers presented here deal with their use and further development.Substantial progress has also been made in the use of the Boundary Element Method for treating crack problems. The inherent mathematical complexity of this method has resulted in somewhat slower progress than that enjoyed by the Finite Element Method and is still the focus of much research. The volume also presents a number of contributions arising from this field. A topic which is closely related to the study of fracture is structural repair. Although repairs are usually effected after fracture occurs, the structural analyst must still ensure that the repair itself is not prone to cracking or other forms of damage. Two approaches to the study of damage in a repaired structure are described in this special volume. These three aspects, taken together, ensure that even the expert will learn something new from this book.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

2D Monolayer MoS2–Carbon Interoverlapped Superstructure: Engineering Ideal Atomic Interface for Lithium Ion Storage: Engineering Ideal Atomic Interface for Lithium Ion Storage

A novel strategy for the controlled synthesis of 2D MoS<inf>2</inf>/C hybrid nanosheets consisting of the alternative layer-by-layer interoverlapped single-layer MoS<inf>2</inf> and mesoporous carbon (m-C) is demonstrated. Such special hybrid nanosheets with a maximized MoS<inf>2</inf>/m-C interface contact show very good performance for lithium-ion batteries in terms of high reversible capacity, excellent rate capability, and outstanding cycling stability.