forthcoming VMPD2015 seminars

[Emanuele Tuillier Illingworth]

Dear all,

this is a list of the forthcoming seminars in the framework of the 
"Variational Methods for Plasticity and Dislocations" intensive period:


*Jean-François Babadjian *
(Université Paris VI - Pierre et Marie Curie)
April 15, 14:00-15:00
SISSA, room 005
Elasto-plasticity models in soil mechanics.

This talk will present elasto-plasticity models arising in soil 
mechanics. Contrary to the typical models mainly used for metals, it is 
required here to take into account plastic dilatancy due to the 
sensitivity of granular materials to hydrostatic pressure. The yield 
criterion thus depends on the mean stress, and the elasticity domain is 
unbounded and not invariant in the direction of hydrostatic matrices. In 
the mechanical literature, so-called cap models have been introduced, 
where the elasticity domain is cut in the direction of hydrostatic 
stresses by means of a strain-hardening yield surface, called a cap. 
Well-posedness results of such models in dynamical and quasi-static 
regimes will be presented, as well as an asymptotic analysis as the cap 
is moved to infinity. It enables one to recover solutions to the 
uncapped model of perfect elasto-plasticity.
Finally, a generalization to non-associative flow rules, where plastic 
flow directions are not necessarily normal to the elasticity set, will 
be presented.


*Peter Hornung*
(TU Dresden)
April 23, 14:00-15:00
SISSA, room 005
TBA
TBA


*Nayam  Al-hassem *
(University of N'djamena)
April 28, 11:00-12:00
SISSA, room 005
A Γ-type estimate for the one-dimensional Allen-Cahn’s action

In this talk we will prove an asymptotic estimate, up to the second 
order included, on the behaviour of the one-dimensional Allen-Cahn's 
action functionals, around a periodic function with bounded variation 
and taking values in {±1}. The leading order term of this estimate 
justifies and confirms, from a variational point of view, the results of 
Fusco-Hale and Carr-Pego on the exponentially slow motion of metastable 
patterns coexisting at the transition temperature.


*Giovanni B. Maggiani *
(Università di Pavia)
May 7, 11:00-12:00
SISSA, room 005
Dynamic evolution of a perfectly plastic plate derived by an asymptotic 
analysis.

We derive a dynamic evolution model for a linearly elastic perfectly 
plastic plate. Starting from the three dimensional dynamic evolution 
problem of Prandtl-Reuss elasto-plasticity with mixed boundary 
conditions , we prove that,  as the thickness of the plate tends to 0, 
the solution converges to a dynamic evolution of a suitable reduced 
model. As in the quasistatic case, the reduced model is purely three 
dimensional and cannot be reduced to a two dimensional setting, then is 
different from the classic two-dimensional problem for thin plates.


*Carolin Kreisbeck *
(Universität Regensburg)
May 14, 16:00-17:00
SISSA, room 005
Homogenization of layered materials with rigid components in single-slip 
finite plasticity.

This talk reports on first progress toward a better quantitative 
understanding of the effective behavior of polycrystalline solids in the 
framework of geometrically nonlinear plasticity. More precisely, we 
study a variational model for plastic material composed of fine parallel 
layers of two types. While one component is completely rigid in the 
sense that it does not admit any plastic deformation but only local 
rotations, the other one is softer featuring a single active slip system 
with linear self-hardening. As a main result, explicit homogenization 
formulas are determined by means of Gamma-convergence. Owing to the 
anisotropic nature of the problem, the findings depend critically on the 
orientation of the layers relative to the slip direction, leading to 
three qualitatively different regimes. In particular, one observes 
macroscopic shearing and blocking effects. The technical difficulties 
are rooted in the intrinsic rigidity resulting from the layered 
geometry, which calls for new rigidity estimates as well as a careful 
analysis of the admissible microstructures restricted by a differential 
inclusion.
This is joint work with Fabian Christowiak (Universität Regensburg).

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