Subject: Applied Maths/Engineering Workshop
are:
26 February 16:10 Applied Maths/Engineering Workshop. Room S/0.38 ENGIN
Speaker: Sam Evans (ENGIN)
Title: Errors and Uncertainties in the Identification of Material Parameters Using nn Inverse FE Approach
Abstract
Soft materials exhibit complex nonlinear mechanical behaviour which is not easily amenable to mathematical modelling. Recently the availability of fast computers and medical imaging techniques has allowed considerable progress in this area, and there are many interesting applications including engineering design, animation and games and medical problems such as surgical planning and navigation.
A major difficulty is the measurement of material properties, which typically requires an "inverse finite element" approach in which a model of an experiment is adjusted to match the experiment in order to identify the material parameters. Often complex material models with many parameters are used, making this a very challenging problem with numerous uncertainties. Although it may be possible to find a set of parameters which matches the experiment reasonably well, it is very difficult to know whether these are the best parameters or what range of other values might be equally good. Typically there are very large uncertainties which are not well understood and cannot easily be quantified. The aim of this study was to develop methods to quantify these uncertainties and identify not just a plausible set of material parameters but also a confidence space, allowing meaningful statistical analysis of the results and a better understanding of the experimental design and optimisation process.
By using Gaussian process models to as emulators for a finite element model it is possible to quantify some of these uncertainties and hence to estimate the overall uncertainty in the identified parameters. Using a Condor network, multiple finite element models were generated and solved in parallel. Gaussian process models were then generated to predict the outputs, errors and variances of these models and hence to carry out a Monte Carlo simulation to quantify the confidence space for the identified parameters.
The actual solution of large deformation, nonlinear finite element models of soft materials is also an open mathematical problem. Current methods derived from linear finite element techniques are slow and unreliable and there is an urgent need for improved algorithms that can provide faster and more reliable convergence. The problem will be discussed in terms of optimisation methods and possible solution schemes using nonlinear conjugate gradient methods will be presented.
