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Dr. Jan Zeman (Czech Technical University, Prague)
| Speaker: |
Dr. Jan Zeman (Czech
Technical University, Prague)
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| Date: |
Wednesday November 11, 2009
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| Title: |
Variational approach
to stable damage evolution in discrete systems
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Abstract
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A consistent derivation of
non-local damage theories for heterogeneous media remains to be of
challenging topics in mechanics of materials. The difficulty of the
subject arises from the fact that the spatial separation of scales,
widely accepted in the well-established homogenization theories, cannot
be applied to the localized damage. In the current presentation, this
limitation is overcome by a careful combination of recent development
in rate independent processes and in Hashin-Shtrikman-Willis
variational principles, specialized to discrete finite systems.
In the adopted rate-independent framework, an analyzed system is
characterized by the total stored elastic energy and the overall energy
dissipation. Following the approach pioneered by Francfort and Marigo,
the damage evolution in a discrete structure follows from as a
time-incremental variational principle, formulated in terms of topology
of damaged phase. The resulting combinatorial optimization problem is
next replaced with a relaxed formulation. The essential ingredient of
this step is a non-local energetic estimate, derived using an
appropriate generalization of the Hashin-Shtrikman variational
principles. Such re-formulation results in an incremental convex
optimization problem, efficiently solvable using linear programming.
Finally, an extension towards stochastic framework will be briefly
commented on. This is a joint work with Ron Peerlings and Marc Geers
(MaTe TU/e).
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