# Young's modulus of rubber sheet using the inflation technique

1. ### Ali Hussain

1
A rubber sheet (thickness 0.2mm) was mounted in an open-type Ussing chamber (6mm aperture) such that hydrostatic pressure could be applied to one side and the resulting inflation of the membrane tracked with an OCT instrument (OCT: ocular coherence tomography). From the geometry of the membrane elevation, I can calculate the elevation at the pole and the arc-length of the capsular segment as a function of applied pressure. Having modeled the system as a spherical segment, the stress was assumed to be σ= PR/2t, where P is the pressure in Pascals, R is the radius of curvature, and t is the thickness of the sample. The Poisson ratio of the sample was determined as 0.47. Could somebody please help me to calculate the Young's modulus of this material using the parameters given earlier. I am trying to use the following equation:

strain (ε)= (σ/E)-μσ/E, where E is Young's Modulus and μ is Poisson's ratio. However, I do not know how to obtain the strain. I have tried to use the arc-length, calculating strain as (l-lo)/lo where l is the measured arc length at a given pressure and lo is the arc-length at zero pressure. But this gives me a value for E that is about 5-fold larger than that obtained using the strip-stretch method. Please, please help. Is it possible to solve this without the use of tensor calculus? Desperately looking forward to a response. Many thanks.