Biomedical Engineering Reference
In-Depth Information
Fig. 1
Cross-section
of
human
femur
showing
trabecular
and
cortical
bone
from
very difficult to predict the behaviour of every crack explicitly in a large popu-
lation of cracks, such as will occur in a typical piece of bone. In such cases the
model must consider the difference in crack locations, sizes, lengths, distribution
and loading conditions.
Existing homogenization theories can be applied in multiscale analysis to assess
the effective properties of a hierarchical material. However, in the non-linear case
it is generally necessary to perform numerical calculation at each iteration for each
structural level, due to the fact that at the micro-level, the homogeneous compo-
nents may change their mechanical behaviour, depending on the stress level
(fracturing, yielding, damage, etc.). This approach becomes expensive in order to
obtain the effective outputs for a global FE model. A more realistic modelling of
physical Cr.Dn and Cr.Le growth within bone must include a multiscale approach
to describe microcrack accumulation from the trabecular level (mesoscopic) to the
whole femur (macroscopic).
Despite progress in the field of bone fatigue modelling, there is still a lack of
models integrating Cr.Dn and Cr.Le accumulation into practical numerical simu-
lation. In the last few years, artificial neural networks (NN) have been used in
many engineering applications as a tool for multiscale analysis to couple models
on different spatial scales, to identify model parameters or to simulate the material
itself. In this paper, a rapid multiscale approach for the simulation of trabecular
bone Cr.Dn and Cr.Le accumulation using hybrid FE analysis and a NN (FENN)
method is developed. The input data for the NN are the applied apparent stress, the
number of cycles, the bone volume fraction (BV
=
TV), the ash density and the
apparent elastic modulus. The output data are the averaged Cr.Dn and Cr.Le at a
specific bone site. First, we show that with a given number of numerical
experiments on a set of different trabecular bone samples, the Cr.Dn and Cr.Le
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