Biomedical Engineering Reference
In-Depth Information
Fig. 8.3
Overview on the coupling of multi-body and FE simulations to achieve efficient for-
ward-dynamics simulations within a continuum-mechanical framework. The coupling is achieved
through a multi-physics nested-iteration approach
If the initial guess is close to the solution, Newton's method converges quadrati-
cally. Second, the initial guess for the nonlinear problem on the finest level is, if
compared with one linearization step at the finest mesh resolution, obtained in a
relative cheap manner as calculations on coarser meshes are much cheaper than on
the finest mesh resolution. This is particularly true for three-dimensional problems.
Such grid-continuation or nested-iteration methods have a great potential for reduc-
ing the number of necessary Newton iterations (Kim et al.,
2006
).
Within the context of modeling a musculoskeletal system, the nested-iteration al-
gorithm as a sequence of predictions on successively finer meshes is extended from
pure mesh refinement to a multi-physics approach. Now, the 'cheapest' solution of
the coarsest mesh is substituted by a different solution methodology, here the rigid-
body dynamics simulations. The key idea hereby is to predict the force and moment
equilibrium within a given musculoskeletal system, i.e. the number of muscles and
their respective levels of activation, using rigid-body dynamics. This procedure is
efficient and, from a computational point of view, relative cheap. The solution of
the multi-body problem serves within the nested-iteration algorithm as reasonable
initial guess for the muscle displacement boundary conditions (still assuming the
bony structures as rigid). Hence, the rigid-body model can be seen as a predictor for
the continuum-mechanical model, and the continuum-mechanical model as a cor-
rector. This way, model-inherent deficiencies of rigid-body dynamics simulations,
e.g., the complex muscle-fiber distributions, contact with other surrounding tissues,
or dynamically changing lines of action can be addressed in an appropriate way. On
the other hand, by predicting an initial guess close to the correct solution, the FE
method's CPU cost can be reduced.
As indicated in Fig.
8.3
, initial tests on integrating such a multi-physics nested-
iteration approach have been carried out on a two-muscle and one-degree of freedom
