Einladung zu einem Vortrag des SFB F013 von:
Dr. Jan Valdmann
(Prag)
Mittwoch, 24. Juli 2002,
13:00 Uhr, KG 712
Multi-yield elastoplasticity: Analysis and Numerics
The aim of this thesis is the mathematical and numerical
analysis of a multi-yield (surface) model in elastoplasticity. The
presented Prandtl-Ishlinskii model of play type generalizes the
linear kinematic hardening model and leads to a more realistic description
of the elastoplastic transition of a material during a deformation
process. The unknowns in the quasi-static formulation are
displacement and (several) plastic strains which satisfy a
time-dependent variational inequality. As for the linear kinematic
hardening model, the variational inequality consists of a bounded and
elliptic bilinear form, a linear functional, and a positive
homogeneous, Lipschitz continuous functional; hence existence and
uniqueness of a weak solution is then concluded from a general
theory.
Our time and space discretization consists of the implicit Euler
method and the lowest order finite element method. For any one-time
step discrete problem, the vector of plastic strains (considered on
one element) depends on the (unknown) displacement only.
In contrast to the linear kinematic hardening model, the dependence
can not be stated explicitly, but has to be calculated by an
iterative algorithm. An a priori error estimate is established
and shows linear convergence with respect to time and space under the
assumption of sufficient regularity of the solution.
A MATLAB solver, which includes the nested iteration technique
combined with an (ZZ-) adaptive mesh-refinement strategy and the
Newton-Raphson method, is employed for solving the two-yield material
model. Various numerical experiments support our theoretical results
and give more insight to complex dynamics in elastoplasticity
problems.
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