Strain fields on cell stressing devices employing clamped circular elastic diaphragms as substrates

Solutions are presented for the surface strain fields on inflated elastomeric circular diaphragms used for in vitro cell stressing experiments. It is shown, by using the method developed by Way (1934) to solve the nonlinear von Karman plate equations, that the surface strains due to bending are not negligible and that large negative radial strains arise near the clamped edge for center deflection-to-thickness ratios (w/h) less than 10. The method of Hart-Smith and Crisp (1967) was used for w/h greater than 10 to solve the nonlinear equations for symmetrical deformation of axially symmetrical rubber-like membranes. In the membrane solutions the circumferential strains drop parabolically to zero at the clamped edge of the diaphragm, while the radial strains increase slightly with the radius. The solutions for w/h greater than 10 are compared to optical measurements of in-plane displacements used to calculate the circumferential strains on the diaphragm, yielding excellent agreement with the theory.