SEMINAIRE D'ANALYSE NUMÉRIQUE
Année universitaire 2017-2018
Jeudi 5 octobre 2017 :
Samir
ADLY
(XLIM, Université de Limoges)
An
implicit sweeping process approach to quasistatic evolution
variational inequalities.
In this talk, we study a new variant of the Moreau's sweeping process with
velocity constraint. Based on an adapted version of the Moreau's catching-up
algorithm, we show the well-posedness (in the sense existence and
uniqueness) of this problem in a general framework. We show the equivalence
between this implicit sweeping process and a quasistatic evolution
variational inequality. It is well-known that the variational formulation of
many mechanical problems with unilateral contact and friction
lead to an evolution variational inequality. As an application, we
reformulate
the quasistatic antiplane frictional contact problem for linear elastic
materials with short memory as an implicit sweeping process with velocity
constraint. The link between the implicit sweeping process and the
quasistatic
evolution variational inequality is possible thanks to some standard
tools from convex analysis and is new in the literature.
