Advancing sport player health with nanocomposite-reinforced shoe soles to enhance dynamic stability

Advancements in nanotechnology have created opportunities to improve both athletic performance and athlete health through the construction of smart materials using enhanced structural design. The present research describes a new method of assisting in the development of athlete health by combining nanocomposite reinforced shoe soles to improve dynamic stability as well as provide transient load resistance to the sole structure. The structure of the shoe sole is modelled as a doubly-curved panel with two radius of curvature parameters, related to a tunnel shape, to replicate the complex geometry of footwear and the interaction with the ground. Graphene oxide powder (GOP) is used as a nanoscaled reinforcement; the homogenized mechanical properties are obtained using the extended Halpin - Tsai method. The equations of motion are derived using first order shear deformation theory (FSDT), while Hamilton's principle produces five coupled partial differential equations representing the vibratory response of the panel. In order to meet simply supported boundary conditions, the displacement fields are expanded using double Fourier trigonometric series according to Navier's solution method. This system provides the dynamic response of the GOP shaped, reinforced soles of shoes when subjected to an active (e.g., impact) force, such as with ground reaction forces during sports activity. The next step in this process will be to apply a Laplace Transform method to solve the equations for the temporal evolution of the materials' displacement and stress. We will use the modified Dubner and Abate Formulation to take the inverse Laplace Transform for the temporal evolution of the materials' displacements and stress. This multi-scale, nano-enabled framework provides a methodology and quantitative measures for optimizing shoe sole design to reduce excessive movement of the foot, decrease the risk of ankle injury, and improve stability in athletes. The data support the potential of nanocomposite designs coupled with advanced continuum mechanics to link advances in nano research to future commercial wearable technology platforms for the improvement of sports health.