Past OxMOS Workshop/Meeting/Lecture

27 May 2008
12:00
Duvan Henao and Xianmin Xu
Abstract
<span style="font-size: x-small; font-family: Arial">Duvan will be talking on &quot;Cavitation, invertibility, and the continuity of the determinant in critical cases&quot;, and Xianmin willl be talking about his work on numerical simulations of cavitation in nonlinear elasticity</span>
  • OxMOS Workshop/Meeting/Lecture
21 May 2008
12:00
William Parnell
Abstract
<em>The effective properties of compos<st1:personname w:st="on">it</st1:personname>e media are defined by the const<st1:personname w:st="on">it</st1:personname>uent phase properties (elastic moduli, thermal conductiv<st1:personname w:st="on">it</st1:personname>ies,etc), their volume fractions, and their distribution throughout the medium. In the case of const<st1:personname w:st="on">it</st1:personname>uents distributed periodically, there exist many homogenization theories which can provide exact solutions for the effective properties. However, the case of the effective properties of random media remains largely an open problem.<o:p></o:p></em> <span style="font-family: Times New Roman"><span style="font-size: 12pt; font-style: italic"><o:p></o:p></span></span><p class="MsoNormal"><span style="font-family: Times New Roman"><span style="font-size: 12pt; font-style: italic">In this talk we will begin by discussing the notion of homogenization as an extension to the continuum assumption and regimes in which <st1:personname w:st="on">it</st1:personname> breaks down. We then discuss various approaches to dealing w<st1:personname w:st="on">it</st1:personname>h randomness whilst determining the effective properties of acoustic, thermal and elastic media.  In particular we show how the effective properties depend on the randomness of the microstructure</span></span></p>
  • OxMOS Workshop/Meeting/Lecture
6 May 2008
15:15
Dr Willam Parnell
Abstract
<span style="color: black">OxMOS vis<st1:personname w:st="on">it</st1:personname>or Dr William Parnell will be introducing his work. This will be followed by an informal tea for anyone who wants to stay on to talk to Dr Parnell.<o:p></o:p></span><span style="color: black"> Further information available from <a href="mailto:OxMOS@maths.ox.ac.uk"><u><span style="color: #0000ff"> OxMOS@maths.ox.ac.uk</span></u></a> Tel 80609<o:p></o:p></span><span style="color: black"><strong>All welcome!<o:p></o:p></strong></span>
  • OxMOS Workshop/Meeting/Lecture
10 March 2008
09:30
to
16:30
Various
Abstract
Fracture mechanics is a significant scientific field of great practical importance. Recently the subject has been invigorated by a number of important accomplishments. From the viewpoint of fundamental science there have been interesting new developments aimed at understanding fracture at the atomic scale; simultaneously, active research programmes have focussed on mathematical modelling, experimentation and computation at macroscopic scales. The workshop aims to examine various different approaches to the modelling, analysis and computation of fracture. The programme will allow time for discussion. Invited speakers include: Andrea Braides (Università di Roma II, Italy) Adriana Garroni (Università di Roma, “La Sapienza”, Italy) Christopher Larsen (Worcester Polytechnic Institute, USA) Matteo Negri (Università di Pavia, Italy) Robert Rudd (Lawrence Livermore National Laboratory, USA)
  • OxMOS Workshop/Meeting/Lecture
28 February 2008
10:00
Abstract
We are concerned with the derivation of the $\Gamma$-limit to a three-dimensional geometrically exact Cosserat model as the relative thickness $h>0$ of a flat domain tends to zero. The Cosserat bulk model involves already exact rotations as a second independent field and this model is meant to describe defective elastic crystals liable to fracture under shear. It is shown that the $\Gamma$-limit based on a natural scaling assumption consists of a membrane like energy contribution and a homogenized transverse shear energy both scaling with $h$, augmented by an additional curvature stiffness due to the underlying Cosserat bulk formulation, also scaling with $h$. No specific bending term appears in the dimensional homogenization process. The formulation exhibits an internal length scale $L_c$ which survives the homogenization process. % A major technical difficulty, which we encounter in applying the $\Gamma$-convergence arguments, is to establish equi-coercivity of the sequence of functionals as the relative thickness $h$ tends to zero. Usually, equi-coercivity follows from a local coerciveness assumption. While the three-dimensional problem is well-posed for the Cosserat couple modulus $\mu_c\ge 0$, equi-coercivity forces us to assume a strictly positive Cosserat couple modulus $\mu_c>0$. The $\Gamma$-limit model determines the midsurface deformation $m\in H^{1,2}(\omega,\R^3)$. For the case of zero Cosserat couple modulus $\mu_c=0$ we obtain an estimate of the $\Gamma-\liminf$ and $\Gamma-\limsup$, without equi-coercivity which is then strenghtened to a $\Gamma$-convergence result for zero Cosserat couple modulus. The classical linear Reissner-Mindlin model is "almost" the linearization of the $\Gamma$-limit for $\mu_c=0$ apart from a stabilizing shear energy term.
  • OxMOS Workshop/Meeting/Lecture

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