Nonlinear Mechanics of a Smart Biotensegrity Human Foot Prosthesis

Abstract

This work deals with the nonlinear mechanics of smart bioinspired tensegrity structures. A minimal regular tensegrity prism actuated by shape memory alloy (SMA) elements is investigated to represent a human foot. A formulation considering the force density matrix approach is used to model the equilibrium equations of the tensegrity structure based on node mapping. Lagrange multipliers are employed to represent constraints. The SMA thermomechanical behavior is described by considering a modified polynomial constitutive model. Numerical simulations are developed from an optimization procedure employing the Levenberg–Marquardt method. An investigation of the tensegrity capability to model a human foot is carried out analyzing either mechanical or physiological aspects of the tensegrity prosthesis. The mechanical performance is compared with high performance prostheses available on the market, showing that it is an interesting alternative with respect to mechanical resistance. Regarding physiology, foot movements are properly mimicked from SMA actuation.