Forthcoming events in this series
OxMOS Workshop: Fracture: modelling, analysis and computation
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)
The $\Gamma$-limit of a finite-strain Cosserat model for asymptotically thin domains versus a formal dimensional reduction
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.
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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.
11:00
High Performance Computational Mechanics in Marenostrum supercomputer
Abstract
Computational Mechanics (CM) has become
a scientific discipline in itself, being High Perfomance Computational
Mechanics (HPCM) a key sub-discipline. The effort for the most efficient use of
distributed memory machines provides a different perspective to CM scientists
relative to a wide range of topics, from the very physics of the problem to
solve to the numerical method used. Marenostrum supercomputer is the largest
facility in Europe and the 5th in the world (top500.org - Spring 2007). This
talk describes the research lines in the CASE Dpt. of the BSC applied to
Aerospace, Bio-mechanics, Geophysics or Environment, through the development of
Alya, the in-house HPCM code for complex coupled problems capable of running
efficiently in large distributed memory facilities.
Phase field modelling and simulation of some interface problems
Abstract
Professor Qiang Du will go over some work on modelling interface/microstructures with curvature dependent energies and also the effect of elasticity on critical nuclei morphology.
OxMOS Lecture - Bifurcation Theory III
Abstract
OxMOS lecture - Bifurcation Theory III
Abstract
OxMOS lecture - Bifurcation Theory II
Abstract
OxMOS Lecture - Bifurcation Theory I
Abstract
OxMOS Team Meeting
Abstract
10:00
Discussion Meeting 3
Abstract
There will be three discussion meetings based on aspects of the
programme open to all internal project members. Others interested in
attending should contact Carlos Mora-Corral.
12:00
Team Meeting
Abstract
Team meetings, held roughly every four weeks, are open to anyone who is
interested. OxMOS post docs and Dphil students will give updates on the
research.
10:00
10:00
14:00
Discussion Meeting 2
Abstract
There will be three discussion meetings based on aspects of the
programme open to all internal project members. Others interested in
attending should contact Carlos Mora-Corral.
12:00
Team Meeting
Abstract
Team meetings, held roughly every four weeks, are open to anyone who is
interested. OxMOS post docs and Dphil students will give updates on the
research.
10:00
10:00
Discussion Meeting 1
Abstract
There will be three discussion meetings based on aspects of the
programme open to all internal project members. Others interested in
attending should contact Carlos Mora-Corral.