Influence of muscle-tendon complex geometrical parameters on modeling passive stretch behavior with the Discrete Element Method

Abstract

The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC's behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young's modulus values of the MTC's components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle's fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure's effects, added to the geometrical parameters, highlight the MTC's mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC's components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements.