Computational modelling of some problems of elasticity and viscoelasticity with applications to thermoforming process

Copyright @ 2012 Northwestern Polytechnical University and ISCIThe reliability of computational models of physical processes has received much attention and involves issues such as the validity of the mathematical models being used, the error in any data that the models need, and the accuracy of the numerical schemes being used. These issues are considered in the context of elastic, viscoelastic and hyperelastic deformation, when finite element approximations are applied. Goal oriented techniques using specific quantities of interest (QoI) are described for estimating discretisation and modelling errors in the hyperelastic case. The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is then treated, with the aim of estimating engineering QoI and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered. The techniques are applied to thermoforming processes where sheets are inflated into moulds to form thin-walled structures

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2013 Walter de Gruyter GmbH.Non-invasive detection, localization and characterization of an arterial stenosis (a blockage or partial blockage in the artery) continues to be an important problem in medicine. Partial blockage stenoses are known to generate disturbances in blood flow which generate shear waves in the chest cavity. We examine a one-dimensional viscoelastic model that incorporates Kelvin–Voigt damping and internal variables, and develop a proof-of-concept methodology using simulated data. We first develop an estimation procedure for the material parameters. We use this procedure to determine confidence intervals for the estimated parameters, which indicates the efficacy of finding parameter estimates in practice. Confidence intervals are computed using asymptotic error theory as well as bootstrapping. We then develop a model comparison test to be used in determining if a particular data set came from a low input amplitude or a high input amplitude; this we anticipate will aid in determining when stenosis is present. These two thrusts together will serve as the methodological basis for our continuing analysis using experimental data currently being collected.National Institute of Allergy and Infectious Diseases, Air Force Office of Scientific Research, Department of Education, and Engineering and Physical Sciences Research Council

Modelling of thermoforming processes for bio-degradable thermoplastic materials

Thin walled container structures have for decades been manufactured from oil based polymeric materials using thermoforming processes. Since the 1980's computational modelling has been used to simulate and aid in the development of these processes. Oil based materials are not eco-friendly, as they do not degrade after use and cause problems of waste. We report here on the computational modelling, using solid mechanics and elasto-plastic deformation, of the thermoforming of food packaging structures made from starch based (bio-degradable) biomaterials. It is shown that, with limited data, it is possible to predict satisfactorily the wall thickness of thermoformed structures. This work was undertaken in BICOM in collaboration with engineering colleagues at Brunel University London, and in association with companies from the polymer industry to provide technical information for their customers

High-order space-time finite element schemes for acoustic and viscodynamic wave equations with temporal decoupling

Copyright @ 2014 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.We revisit a method originally introduced by Werder et al. (in Comput. Methods Appl. Mech. Engrg., 190:6685–6708, 2001) for temporally discontinuous Galerkin FEMs applied to a parabolic partial differential equation. In that approach, block systems arise because of the coupling of the spatial systems through inner products of the temporal basis functions. If the spatial finite element space is of dimension D and polynomials of degree r are used in time, the block system has dimension (r + 1)D and is usually regarded as being too large when r > 1. Werder et al. found that the space-time coupling matrices are diagonalizable over inline image for r ⩽100, and this means that the time-coupled computations within a time step can actually be decoupled. By using either continuous Galerkin or spectral element methods in space, we apply this DG-in-time methodology, for the first time, to second-order wave equations including elastodynamics with and without Kelvin–Voigt and Maxwell–Zener viscoelasticity. An example set of numerical results is given to demonstrate the favourable effect on error and computational work of the moderately high-order (up to degree 7) temporal and spatio-temporal approximations, and we also touch on an application of this method to an ambitious problem related to the diagnosis of coronary artery disease

Conforming finite element methods for the clamped plate problem

Finite element methods for solving biharmonic boundary value problems are considered. The particular problem discussed is that of a clamped thin plate. This problem is reformulated in a weak, form in the Sobolev space Techniques for setting up conforming trial Functions are utilized in a Galerkin technique to produce finite element solutions. The shortcomings of various trial function formulations are discussed, and a macro—element approach to local mesh refinement using rectangular elements is given

SiDCoN: A Tool to Aid Scoring of DNA Copy Number Changes in SNP Chip Data

The recent application of genome-wide, single nucleotide polymorphism (SNP) microarrays to investigate DNA copy number aberrations in cancer has provided unparalleled sensitivity for identifying genomic changes. In some instances the complexity of these changes makes them difficult to interpret, particularly when tumour samples are contaminated with normal (stromal) tissue. Current automated scoring algorithms require considerable manual data checking and correction, especially when assessing uncultured tumour specimens. To address these limitations we have developed a visual tool to aid in the analysis of DNA copy number data. Simulated DNA Copy Number (SiDCoN) is a spreadsheet-based application designed to simulate the appearance of B-allele and logR plots for all known types of tumour DNA copy number changes, in the presence or absence of stromal contamination. The system allows the user to determine the level of stromal contamination, as well as specify up to 3 different DNA copy number aberrations for up to 5000 data points (representing individual SNPs). This allows users great flexibility to assess simple or complex DNA copy number combinations. We demonstrate how this utility can be used to estimate the level of stromal contamination within tumour samples and its application in deciphering the complex heterogeneous copy number changes we have observed in a series of tumours. We believe this tool will prove useful to others working in the area, both as a training tool, and to aid in the interpretation of complex copy number changes

Income differences in food consumption in the 1995 Australian national nutrition survey

Objective: To assess the relationships between an index of per capita income and the intake of a variety of individual foods as well as groups of food for men and women in different age groups. Design: Cross-sectional national survey of free-living men and women. Subjects: A sample of 5053 males and 5701 females aged 18 y and over who completed the Australian National Nutrition Survey 1995. Methods: Information about the frequency of consumption of 88 food items was obtained. On the basis of scores on the Food Frequency Questionnaire, regular and irregular consumers of single foods were identified. The relationships between regularity of consumption of individual foods and per capita income were analysed via contingency tables. Food variety scores were derived by assigning individual foods to conventional food group taxonomies, and then summing up the dichotomised intake scores for individual foods within each food group. Two-way ANOVA (income age group) were performed on the food variety scores for males and females, respectively. Results: Per capita income was extensively related to the reported consumption of individual foods and to total and food group variety indices. Generally, both men and women in low income households had less varied diets than those in higher-income households. However, several traditional foods were consumed less often by young high-income respondents, especially young women. Conclusions: Major income differentials in food variety occur in Australia but they are moderated by age and gender. Younger high-income women, in particular, appear to have rejected a number of traditional foods, possibly on the basis of health beliefs. The findings also suggest that data aggregation has marked effects on income and food consumption relationships.<br /