Use of hyperelastic models and sliding connections to model the mechanical behavior of musculoskeletal structures

Resumo

The generation of movement and force produced by the musculoskeletal system in various parts of the body is a topic of high interest in academic research. The increasingly detailed and precise knowledge of the biomechanical behavior of these structures is required to meet the demands of health care and human well-being. The use of structural analysis tools is essential for that purpose. In some situations, in vivo or in vitro tests present a series of inconveniences; therefore, computational simulations prove to be complementary to experimental tests to analyze human movements and generally offer advantages in terms of cost and time. To contribute to the construction of a more precise understanding of the mechanical behavior of biological structures, this work aims to numerically simulate the planar behavior of the upper limb of the human body through the action of skeletal muscles and the movement of adjacent joints. The mechanical simulation is performed through a computational code developed based on the Positional Finite Element Method (PFEM), capable of performing geometric nonlinear analyses directly in its formulation. The proposed modeling treats the muscle tissue as a composite material made of a three-dimensional matrix and embedded simple bar elements, which represent the muscle fibers. Despite the three-dimensional nature of the model, it is important to emphasize that the work aims at a two-dimensional application, simulating the mechanical behavior of musculoskeletal structures on a single plane. The Saint-Venant-Kirchhoff hyperelastic constitutive model is used to define the relationship between stresses and strains in the materials, highlighting its potential and limitations. Additionally, the active muscle behavior is considered through a numerical strategy that represents fiber contraction by allows controlling the initial length of the bar element. The joint studied in the model is the elbow, modeled through the formulation of sliding connections, allowing relative movement between connected surfaces. Since the mechanical simulation is planar, only flexion and extension movements are reproduced. The kinematic conditions imposed on the system to promote sliding are introduced into the problem using Lagrange multipliers. The proposed model has the potential to describe the mechanical response of human body members in a simplified manner.