Skeletal muscle: Modeling the mechanical behavior by taking the hierarchical microstructure into account

Skeletal muscles ensure the mobility of mammals and are complex natural fiber-matrix-composites with a hierarchical microstructure. In this work, we analyze the muscle's mechanical behavior on the level of fascicles and muscle fibers. We introduce continuum mechanics hyperelastic material models for the connective tissue endomysium and the embedded muscle fibers. The coupled electrical, chemical and mechanical processes taking place in activated contracting muscle fibers are captured including the temporal change of the activation level and the spatial propagation of the activation potential in fibers. In our model, we investigate the material behavior of fascicle, fiber and endomysium in the fiber direction and examine interactions between muscle fiber and endomysium by considering the temporal and spatial change of muscle fiber activation. In addition, a loading case of normal and shear forces is applied to analyze the fiber lifting force and the lifting height of unipennate muscles with different pennation angles. Moreover, the development of local stresses and strains in fibers and endomysium for different strains are studied. The simulation results allow to identify regions in high risk of damage. Optimal arrangements of unipennate muscle microstructure are found for either very small or very large pennation angles.