MAFELAP 2013 presentation

Stéphane P. A. Bordas

http://people.brunel.ac.uk/~icsrsss/bicom/mafelap2013/
 

"Advances in extended finite element methods for fracture and heterogeneous materials"

This presentation will address recent advances in enriched numerical methods to simplify the treatment of evolving discontinuities in the field variables or their derivatives: cracks or material interfaces; and to treat geometrically intricate domains and their evolution.

The presentation will be composed of three parts:

(1) advances in numerical methods aiming at simplifying the treatment of complex geometries;

Two competing approaches coexist in the literature to simplify the solution of partial differential equations over domains of complex and/or evolving geometries. One focuses on streamlining the transition between computer aided design (CAD) data and the solution of problems over the corresponding domains. An example of this is isogeometric analysis (Hughes et al. 2005) where the geometry description and the approximation of the field variables are tied, thus enabling an exact treatment of the boundary as well as simplifying eventual geometric design iterations.
The second approach follows an orthogonal direction, where the geometry is uncoupled from the field variable discretisation, e.g. embedded boundary methods such as the structured extended finite element method of (Belytschko et al. 2003).
We will present results emanating from both lines of thought: isogeometric analysis of three-dimensional structures and embedded interfaces for complex geometries including sharp edges and vertices.

(2) advances in enriched formulations for evolving discontinuities such as cracks

The extended finite element method (XFEM) was introduced in (Belytschko and Black, 1999), with, as a basis, the partition of unity enrichment method of (Melenk and Babuška, 1996). The XFEM enables the simulation of evolving discontinuities without or with minimal remeshing.
We present recent developments in the area and focus on tackling difficulties associated with the control of the conditioning number of the system, the control of the error in quantities of interest, element distortion and blending errors between different partitions of unity.

(3) applications of those methods to problems in Silicon wafer manufacturing and brain surgery simulation.

Finally, as an application, we will present a simple method to grow several hundreds of cracks in two-dimensions in order to predict their growth and coalescence in brittle materials using the XFEM.
We will also present recent results permitting the simulation of cutting and contact during brain surgery simulation at 30 frames per second using an implicit time integration method and a hybrid, asynchronous CPU/GPU solver.

We finish the presentation by conclusions and propositions for future work.

Acknowledgements: Stéphane P.A. Bordas wishes to thank the organisers of MAFELAP for their kind invitation. He is grateful to the European Research Council for funding the research presented (ERC Stg grant agreement No. 279578: "RealTCut Towards real time multiscale simulation of cut- ting in non-linear materials with applications to surgical simulation and computer guided surgery").

Isogeometric analysis of large deformation of a cylinder shell. Done in jem/jive C++ code. Visualization done in Paraview.

Isogeometric Analysis of a cantilever beam with large displacement and rotation. Performed with MIGFEM--an IGA FEM code that is free for download at https://sourceforge.net/projects/cmcodes/

SIAM National Student Chapter Conference 2013

Subject: SIAM National Student Chapter Conference 2013

A reminder that Registration is now open for participation in the annual SIAM National Student Chapter Conference to take place in Warwick on the 10th of May 2013:

 

http://www2.warwick.ac.uk/fac/sci/maths/postgrad/siamstudentchapter/home/snscc/

 

The abstracts for the invited lectures are already available there and look really interesting!!

 

Plenary Talks:

• Accuracy and Reproducibility of Numerical Computations, Nicholas J. Higham - University of Manchester
• Magnetic chains: from self-buckling to self-assembly, Alain Goriely - University of Oxford
• Phase transitions and computational tractability, Mark Jerrum - Queen Mary, University of London

Sponsor Talks:

• Implementing Algorithms: the link between academia and industry, Edvin Deadman, The Numerical Algorithms Group (NAG)

 

 

The deadline for submission of a title/abstract for a short talk (20min) or a poster is 19 April.  

Applied Maths/Engineering Seminar - TODAY

Seminar today - Tuesday 19th March 2013 at 16:10 in M/2.06 (MATHS)

Speaker: Prof Serafim Kalliadasis (Imperial).

Title: Recent progress on the moving contact line problem.

Abstract: The moving contact line problem is a long-standing and fundamental challenge in the field of fluid dynamics, occurring when one fluid replaces another as it moves along a solid surface. Moving contact lines occur in a vast range of applications, where an apparent paradox of motion of a fluid-fluid interface, yet static fluid velocity at the solid satisfying the no-slip boundary condition arises. In this talk we will review recent progress on the problem made by our group.

The motion of a contact line is examined, and comparisons drawn, for a variety of proposed models in the literature. We first scrutinise a number of models in the classic test-bed system of spreading of a thin two-dimensional droplet on a planar substrate, showing that slip, precursor film and interface formation models effectively reduce to the same spreading behaviour. This latter model, developed by Shikhmurzaev a few years ago, is a complex and somewhat controversial one, differentiating itself by accounting for a variation in surface layer quantities and having finite-time surface tension relaxation. Extensions to consider substrate heterogeneities in this prototype system for slip models are also considered, such as for surface roughness and fluctuations in wetting properties through chemical variability. Analysis of a solid-liquid-gas diffuse-interface model is then presented, with no-slip at the solid and where the fluid phase is specified by a continuous density field. We first obtain a wetting boundary condition on the solid that allows us to consider the motion without any additional physics, i.e. without density gradients at the wall away from the contact line associated with precursor films.

Careful examination of the asymptotic behaviour as the contact line is approached is then shown to resolve the singularities associated with the moving contact line problem. Various features of the model are scrutinised alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall. But these are not necessary to resolve the moving contact line problem.

Tea/coffee will be available in the UCAS Room afterwards

Applied Maths/Engineering Workshop - TODAY

Subject: Applied Maths/Engineering Workshop - TODAY

Tuesday 5th March

16:10 Applied Mathematics/Engineering Research Workshop: Room M/2.06

Speaker: Maurice Blount (MATHS)
Title: The adhesion and desiccation of a sessile vesicle

Abstract:
Anhydrobiosis is a proposed method of preserving biological material through drying it rather than freezing it.  To understand aspects of this process, I model the cell as a semi-permeable elastic membrane (a vesicle), and first apply a long-wave approximation to describe the drying process in regimes where the vesicle is strongly adhered to a substrate.  The results of this simplified model are compared with those of boundary-integral simulations, and I analyse the latter to show how the process of vesicle adhesion depends strongly on the thin layer of fluid that is trapped between the vesicle and the substrate.

Applied Maths/Engineering Workshop

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.