Effect of Simulated Mass-Tunable Auxetic Midsole on Vertical Ground Reaction Force

Abstract

When runners impact the ground, they experience a sudden peak ground reaction force (GRF), which may be up to 4× greater than their bodyweight. Increased GRF impact peak magnitude has been associated with lower limb injuries in runners. Yet, shoe midsoles are capable of cushioning the impact between the runner and the ground to reduce GRF. It has been proposed that midsoles should be tunable with subject mass to minimize GRF and reduce risk of injury. Auxetic metamaterials, structures designed to achieve negative Poisson's ratios, demonstrate superior impact properties and are highly tunable. Recently, auxetic structures have been introduced in footwear, but their effects on GRF are not documented in literature. This work investigates the viability of a three-dimensional auxetic impact structure with a tunable force plateau as a midsole through mass-spring-damper simulation. An mass-spring-damper model was used to perform 315 simulations considering combinations of seven subject masses (45–90 kg), 15 auxetic plateau forces (72–1080 N), and three auxetic damping conditions (450, 725, and 1000 Ns/m) and regression analysis was used to determine their influence on GRF impact peak, energy, instantaneous, and average loading rate. Simulations showed that tuning auxetic plateau force and damping based on subject mass may reduce GRF impact and loading rate versus simulated conventional midsoles. Auxetic plateau force and damping conditions of 450 Ns/m and ∼1 bodyweight (BW), respectively, minimized peak impact GRF. This work demonstrates the need for tunable auxetic midsoles and may inform future work involving midsole testing.