Multi-scale Smoothed Finite Element
Title Alternative:Micro-mechanical Material Analysis
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Date
2019
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Abstract
Simulations in material engineering must consider complex physical phenomena
that have a non-linear character and interact with multiple time and
space scales. In spite of the intensive development of computational technologies,
spatial and temporal simulations penetrating signi cantly di erent
scales, starting with the electron structure and visible at the end, can still
be realized only very limited. This work is devoted to multi-scale homogenization
starting from mathematical formulation and ends up with the construction
of a model derived from real data. The rst part introduces a new
implementation of periodic boundary conditions in the sense of the Nitsche's
method and subsequently tested on complex material structures. The second
part introduces the gradient smoothing technique and its use to improve the
convergence properties of the nite element method and the accuracy of the
estimation of the e ective material properties. The third part is devoted
to the e ective reconstruction of brous textile structures from tomographic
data including the estimation of morphological parameters.
Description
habilitační práce
Subject(s)
periodic boundary conditions, nite element method, multi-scale modelling, gradient smoothing, Nitsche's method, micro CT, image analysis