Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.

Thermal-mechanical modelling of power electronic module packaging

In this paper the reliability of the isolation substrate and chip mountdown solder interconnect of power modules under thermal-mechanical loading has been analysed using a numerical modelling approach. The damage indicators such as the peel stress and the accumulated plastic work density in solder interconnect are calculated for a range of geometrical design parameters, and the effects of these parameters on the reliability are studied by using a combination of the finite element analysis (FEA) method and optimisation techniques. The sensitivities of the reliability of the isolation substrate and solder interconnect to the changes of the design parameters are obtained and optimal designs are studied using response surface approximation and gradient optimization method

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

The application of free-surface techniques to metal forming processes

In this paper the use of free-surface techniques, within the framework of a finite volume methodology, are investigated for the simulation of metal forming processes. In such processes, for example extrusion and forging, a workpiece is subjected to large scale deformation to create the product's shape. The use of Eulerian free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remmeshing. Two free-surface techniques to predict this final shape offers the advantage, over the traditionally used Lagrangian finite element method, of not requiring remesingh. Two free-surface techniques are compared by modelling a typical example of this type of process - non-Newtonian extrusion of an aluminium workpiece through a conical die.

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.

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.

Modelling the Performance of Flexible Substrates for Lead-Free Applications

In this paper, the performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track. Secondly, an ACF flip chip was taken as a typical lead-free application of the flex substrate. The reflow effect on the reliability of ACF interconnections was analyzed. Higher stress was identified along the interface between the conductive particle and the metallization, and the interfacial stress increases with the reflow peak temperature and the coefficient of thermal expansion (CTE) of the adhesive. The moisture effect on the reliability of ACF joints were studied using a macro-micro modeling technique, the predominantly tensile stress found at the interface between the conductive particle and metallization could reduce the contact area and even cause the electrical failure. Modeling results are consistent with the findings in the experimental work

Analyzing the performance of flexible substrates for lead-free applications

The performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track and the thickness of the flex. Secondly, an anisotropic conductive film (ACF) flip chip was taken as a typical lead-free application of the flex substrate and the moisture effect on the reliability of ACF joints were studied using a 3D macro-micro modeling technique. It is found that the time to be saturated of an ACF flip chip is much dependent on the moisture diffusion rate in the polyimide substrate. The majority moisture diffuses into the ACF layer from the substrate side rather than the periphery of the ACF. The moisture induced stress was predicted and the predominant tensile stress was found at the interface between the conductive particle and metallization which could reduce the contact area and even cause the electrical failure

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution