This paper presents a novel fiber-based muscle model for the forward dynamics of the musculoskeletal system. While bones are represented by rigid bodies, the muscles are taken into account by means of one-dimensional cables that obey the laws of continuum mechanics. In contrast to standard force elements such as the Hill-type muscle model, this approach is close to the real physiology and also avoids the issue of wobbling masses. On the other hand, the computational cost is rather low in comparison with full 3D continuum mechanics simulations. The cable model includes sliding contact between individual fibers as well as between fibers and bones. For the discretization, cubic finite elements are employed in combination with implicit time stepping. Several validation studies and the simulation of a motion scenario for the upper limb demonstrate the potential of the fiber-based approach.
We present high order surface finite element methods for the linear analysis of seven-parameter shells. The special feature of these methods is that they work with the exact geometry of the shell reference surface which can be given parametrically by a global map or implicitly as the zero level-set of a level set function. Furthermore, a special treatment of singular parametrizations is proposed. For the approximation of the shell displacement parameters we have implemented arbitrary order hierarchical shape functions on quadrilateral and triangular meshes. The methods are verified by a convergence analysis in numerical experiments.
The construction of volumetric parametrizations for computational domains is a key step in the pipeline of isogeometric analysis. Here, we investigate a solution to this problem based on the mesh deformation approach. The desired domain is modeled as a deformed configuration of an initial simple geometry. Assuming that the parametrization of the initial domain is bijective and that it is possible to find a locally invertible displacement field, the method yields a bijective parametrization of the target domain. We compute the displacement field by solving the equations of nonlinear elasticity with the neo-Hookean material law, and we show an efficient variation of the incremental loading algorithm tuned specifically to this application. In order to construct the initial domain, we simplify the target domain's boundary by means of an L 2 -projection onto a coarse basis and then apply the Coons patch approach. The proposed methodology is not restricted to a single patch scenario but can be utilized to construct multi-patch parametrizations with naturally looking boundaries between neighboring patches. We illustrate its performance and compare the result to other established parametrization approaches on a range of two-dimensional and three-dimensional examples.
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