Visualisation of numerical models for paper damage mechanics

Abstract not available

Review of methods to predict solder joint reliability under thermo-mechanical cycling

Solder joints are often the cause of failure in electronic devices, failing due to cyclic creep induced ductile fatigue. This paper will review the modelling methods available to predict the lifetime of SnPb and SnAgCu solder joints under thermo-mechanical cycling conditions such as power cycling, accelerated thermal cycling and isothermal testing, the methods do not apply to other damage mechanisms such as vibration or drop-testing. Analytical methods such as recommended by the IPC are covered, which are simple to use but limited in capability. Finite element modelling methods are reviewed, along with the necessary constitutive laws and fatigue laws for solder, these offer the most accurate predictions at the current time. Research on state-of-the-art damage mechanics methods is also presented, although these have not undergone enough experimental validation to be recommended at present

Modelling continuum mechanics phenomena using three dimensional unstructured meshes on massively parallel processors

The difficulties encountered in implementing large scale CM codes on multiprocessor systems are now fairly well understood. Despite the claims of shared memory architecture manufacturers to provide effective parallelizing compilers, these have not proved to be adequate for large or complex programs. Significant programmer effort is usually required to achieve reasonable parallel efficiencies on significant numbers of processors. The paradigm of Single Program Multi Data (SPMD) domain decomposition with message passing, where each processor runs the same code on a subdomain of the problem, communicating through exchange of messages, has for some time been demonstrated to provide the required level of efficiency, scalability, and portability across both shared and distributed memory systems, without the need to re-author the code into a new language or even to support differing message passing implementations. Extension of the methods into three dimensions has been enabled through the engineering of PHYSICA, a framework for supporting 3D, unstructured mesh and continuum mechanics modeling. In PHYSICA, six inspectors are used. Part of the challenge for automation of parallelization is being able to prove the equivalence of inspectors so that they can be merged into as few as possible.

Segregation predictions for a binary mixture of granular material under flow conditions in a continuum mechanics framework

Abstract not available

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.

Micro-mechanical parameterisations for continuum modelling of granular material using the discrete element method

The present work uses the discrete element method (DEM) to describe assemblies of particulate bulk materials. Working numerical descriptions of entire processes using this scheme are infeasible because of the very large number of elements (1012 or more in a moderately sized industrial silo). However it is possible to capture much of the essential bulk mechanics through selective DEM on important regions of an assembly, thereafter using the information in continuum numerical descriptions of particulate processes. The continuum numerical model uses population balances of the various components in bulk solid mixtures. It depends on constitutive relationships for the internal transfer, creation and/or destruction of components within the mixture. In this paper we show the means of generating such relationships for two important flow phenomena – segregation whereby particles differing in some important property (often size) separate into discrete phases, and degradation, whereby particles break into sub-elements, through impact on each other or shearing. We perform DEM simulations under a range of representative conditions, extracting the important parameters for the relevant transfer, creation and/or destruction of particles in certain classes within the assembly over time. Continuum predictions of segregation and degradation using this scheme are currently being successfully validated against bulk experimental data and are beginning to be used in schemes to improve the design and operation of bulk solids process plant.

Analysis and modeling of heaping behavior of granular mixtures within a computational mechanics framework

This paper presents a continuum model of the flow of granular material during filling of a silo, using a viscoplastic constitutive relation based on the Drucker-Prager plasticity yield function. The performed simulations demonstrate the ability of the model to realistically represent complex features of granular flows during filling processes, such as heap formation and non-zero inclination angle of the bulk material-air interface. In addition, micro-mechanical parametrizations which account for particle size segregation are incorporated into the model. It is found that numerical predictions of segregation phenomena during filling of a binary granular mixture agree well with experimental results. Further numerical tests indicate the capability of the model to cope successfully with complex operations involving granular mixtures.

Identifying the damage mechanisms in paper using the acoustic emission monitoring technique

This paper investigates the use of the acoustic emission (AE) monitoring technique for use in identifying the damage mechanisms present in paper associated with its production process. The microscopic structure of paper consists of a random mesh of paper fibres connected by hydrogen bonds. This implies the existence of two damage mechanisms, the failure of a fibre-fibre bond and the failure of a fibre. This paper describes a hybrid mathematical model which couples the mechanics of the mass-spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. The derivation of the mass-spring model can be found in [1,2], with details of the acoustic wave equation found in [3,4]. The numerical implementation of the vibro-acoustic model is discussed in detail with particular emphasis on the damping present in the numerical model. The hybrid model uses an implicit solver which intrinsically introduces artificial damping to the solution. The artificial damping is shown to affect the frequency response of the mass-spring model, therefore certain restrictions on the simulation time step must be enforced so that the model produces physically accurate results. The hybrid mathematical model is used to simulate small fibre networks to provide information on the acoustic response of each damage mechanism. The simulated AEs are then analysed using a continuous wavelet transform (CWT), described in [5], which provides a two dimensional time-frequency representation of the signal. The AEs from the two damage mechanisms show different characteristics in the CWT so that it is possible to define a fibre-fibre bond failure by the criteria listed below. The dominant frequency components of the AE must be at approximately 250 kHz or 750 kHz. The strongest frequency component may be at either approximately 250 kHz or 750 kHz. The duration of the frequency component at approximately 250 kHz is longer than that of the frequency component at approximately 750 kHz. Similarly, the criteria for identifying a fibre failure are given below. The dominant frequency component of the AE must be greater than 800 kHz. The duration of the dominant frequency component must be less than 5.00E-06 seconds. The dominant frequency component must be present at the front of the AE. Essentially, the failure of a fibre-fibre bond produces a low frequency wave and the failure of a fibre produces a high frequency pulse. Using this theoretical criteria, it is now possible to train an intelligent classifier such as the Self-Organising Map (SOM) [6] using the experimental data. First certain features must be extracted from the CWTs of the AEs for use in training the SOM. For this work, each CWT is divided into 200 windows of 5E-06s in duration covering a 100 kHz frequency range. The power ratio for each windows is then calculated and used as a feature. Having extracted the features from the AEs, the SOM can now be trained, but care is required so that the both damage mechanisms are adequately represented in the training set. This is an issue with paper as the failure of the fibre-fibre bonds is the prevalent damage mechanism. Once a suitable training set is found, the SOM can be trained and its performance analysed. For the SOM described in this work, there is a good chance that it will correctly classify the experimental AEs.

On the continuum modelling of granular flows with the aid of micro-mechanical parametrisations

Abstract not available

Dynamic load balancing of distributed memory parallel computational mechanics using unstructured meshes for multi-physical modelling

As the complexity of parallel applications increase, the performance limitations resulting from computational load imbalance become dominant. Mapping the problem space to the processors in a parallel machine in a manner that balances the workload of each processors will typically reduce the run-time. In many cases the computation time required for a given calculation cannot be predetermined even at run-time and so static partition of the problem returns poor performance. For problems in which the computational load across the discretisation is dynamic and inhomogeneous, for example multi-physics problems involving fluid and solid mechanics with phase changes, the workload for a static subdomain will change over the course of a computation and cannot be estimated beforehand. For such applications the mapping of loads to process is required to change dynamically, at run-time in order to maintain reasonable efficiency. The issue of dynamic load balancing are examined in the context of PHYSICA, a three dimensional unstructured mesh multi-physics continuum mechanics computational modelling code.