An original approach to generate periodic Representative Volume Elements with anisotropic heterogeneous microstructure: application to skeletal muscle.

Skeletal muscle is an organ whose hierarchical, multiscale structure greatly influences the overall mechanical response. Complementary to mechanical experiments, finite element modeling is increasingly used to study the influence of its constituents across different scales. To develop such a multiscale model, particular attention must be paid not only to the scale transition, but also to the definition of the structure and its mechanical behavior at different scales (macroscopic, microscopic, submicron). One of the most effective approaches is to define a Representative Volume Element (RVE) including smaller scale components and their respective mechanical behavior laws, likely to be altered through pathologies. In this study, an original approach for periodic RVE generation dedicated to multiscale modeling of the skeletal muscle is proposed. From optical microscopy cross-section images of mouse skeletal muscle and single fiber experiments, the RVE integrates parameters related to fiber type distribution, geometric and mechanical characteristics. The key features of this geometry are spatial periodicity, rounded edges and inclusion of experimentally measured probabilistic distributions of the extracellular matrix (ECM), slow and fast muscle fibers. Smooth variation of the mechanical properties between the muscle fibers and the ECM are implemented to avoid unrealistic and purely numerical stress accumulation at these interfaces through the definition of transition layers between the different microcomponents. By the inclusion of custom geometrical and material features, this original model allows the multiscale and multicomponent analysis of different muscle phenotypes and can also be used for other heterogeneous anisotropic materials such as fiber reinforced composites.