Mathematical Model for the Determination of The Young’s Modulus of Polyurethane (PU) and Polyvinyl Chloride (PVC) Hearing Protectors

Personal hearing protectors are tools that improve the conditions of workers. In order to study their efficiency and decrease the hearing lose. A finite elements method is presented in this work in order to give a physical characterization of hearing protectors materials. In harmony with the simplified model of Sessler [1] and for a better understanding of the studied materials behavior, we present in this work a new analytical model based on the assumption of the regular pores distribution in the polymer material. Given the scarcity of studies reporting the mechanical behavior of foams as a function of pore distribution and given that theoretical models do not predict any dependence of Young’s modulus with pore distribution and pore size, The aim of this work will be to determine the expression of Young’s modulus as a function of material parameters and matrix properties. These parameters will be used in the modeling of the mechanical behavior of a porous polymers sample based on polyurethane (PU) and polyvinyl chloride (PVC). This behavior model which depends on porosity and other factors affecting the porous character will allow to determine the sound absorption, transmission and reflection coefficients. It is important to mention that the theoretical value of Young’s modulus is based on the assumptions of elasticity theory.