Mathematical Modelling of Structures, Solids and Fluids
http://hdl.handle.net/2160/2918
2014-04-24T04:55:26ZExact solution to a refined contact problem for biphasic cartilage layers
http://hdl.handle.net/2160/11052
Exact solution to a refined contact problem for biphasic cartilage layers
Argatov, Ivan; Mishuris, Gennady
Nithiarasu, P; Lohner, R; van Loon, R
We revisit the axisymmetric contact problem for a biphasic cartilage layer and consider a refined formulation taking into account the both normal and tangential displacements at the contact interface. The obtained analytical solution is valid for arbitrary time and increasing loading conditions. We compare it with the classic result and indicate cases where the difference could be pronounced.
Mishuris, G; Argatov I. Exact solution to a refined contact problem for biphasic cartilage layers. In proceedings of First International Conference on Computational and Mathematical Biomedical Engineering (CMBE09), Eds. P. Nithiarasu, R. Lohner, R. van Loon, ISBN:978-0-9562914-0-0 Swansea, Swansea, June 2009, pages 151 - 154.
2009-06-01T00:00:00ZTopological and geometrical disorder correlate robustly in two-dimensional foams
http://hdl.handle.net/2160/10909
Topological and geometrical disorder correlate robustly in two-dimensional foams
Cox, Simon; Kafer, J.; Rabaud, D.; Quilliet, C.; Graner, François; Ataei Talebi, S.
A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.
Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes C. Quilliet, S. Ataei Talebi, D. Rabaud, J. Kafer, S.J. Cox and F. Graner (2008) Topological and geometrical disorder correlate robustly in two-dimensional foams. Sponsorship: We thank J. Legoupil for his participation in the simulations, K. Brakke for developing and maintaining the Surface Evolver code, A.F.M. Maree for developing the Potts model code used here, M.F. Vaz for providing references, I. Cantat for critical reading of the manuscript, Y. Bella¨ıche, R. Carthew and T. Hayashi for providing pictures of biological tissues, S. Courty for their analysis, P. Ballet for help in setting up the experiment, and participants of the Foam Mechanics workshop (Grenoble, January 2008) for many discussions. S.A.T. thanks Dr Ejtehadi for hospitality at the Institute of Physics and Mathematics, Tehran (Iran). S.J.C. thanks UJF for hospitality, and CNRS, EPSRC (EP/D048397/1, EP/D071127/1) and the British Council Alliance scheme for financial support.
2008-01-01T00:00:00ZSimulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs
http://hdl.handle.net/2160/10896
Simulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs
Wyn, Aled; Davies, Ioan Tudur; Cox, Simon John
Surface Evolver simulations of flowing two-dimensional foams are described. These are used for two purposes. Firstly, to extract the location of the T1s, the changes in bubble topology that occur during plastic flow. It is shown that the T1s are localized in space, becoming more so as the polydispersity of the foam decreases. Secondly, the sedimentation of two circular discs through a foam under gravity is studied. If the discs are sufficiently close, they begin to interact and one moves behind the other during their descent.
Wyn, A., Davies, I. T., Cox, S. J. (2008). Simulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs. European Physical Journal E, 26 (1-2), 81-89. Sponsorship: We thank K. Brakke for developing, dis-tributing and supporting the Surface Evolver and for providing the script to generate Voronoi input. This work benefited from discussions with D. Weaire, K. Krishan and F. Graner. Financial support is gratefully acknowledged from EPSRC (EP/D048397/1,EP/D071127/1) and the British Council Alliance programme.
2008-04-11T00:00:00ZScreening in dry two-dimensional foams
http://hdl.handle.net/2160/10895
Screening in dry two-dimensional foams
Cox, Simon; Graner, François; Vaz, M. Fatima
Using the Surface Evolver software, we perform numerical simulations of point-like deformations in a two-dimensional foam. We study perturbations which are infinitesimal or finite, isotropic or anisotropic, and we either conserve or do not conserve the number of bubbles. We measure the displacement fields around the perturbation. Changes in pressure decrease exponentially with the distance to perturbation, indicating a screening over a few bubble diameters.
S.J. Cox, F. Graner and M.F. Vaz (2008) Screening in dry two-dimensional foams. Soft Matter, 4:1871-1878 The full text in the repository will be available from 4 October 2009 in accordance with the publisher's embargo policy Sponsorship: We thank S. Courty, E.H.M. Guene, E. Janiaud, J. K¨afer, J. Lambert, M.Mancini and other participants in the Grenoble Foam Mechanics Workshop for stimulation and useful discussions. We thank K. Brakke for his development and maintenance of the Surface Evolver code. SJC thanks the British Council Alliance programme, CNRS and EPSRC (EP/D048397/1,EP/D071127/1) for financial support and UJF for hospitality during the period in which this work was conceived.
2008-01-01T00:00:00Z