A new analytical solution for the load-deflection of square membranes

Dual Diaphragm based Cantilever Operated Mechatronic Differential Pressure Sensor and Transmitter

“…A thin metallic diaphragm having elastic properties undergoes changes in its surface when force is applied on it [8][9][10]. This change in deformation depends on the geometrical size and boundary conditions.…”

Characterization of W Films on Si and SiO2/Si Substrates by X-Ray Diffraction, AFM and Blister Test Adhesion Measurements

“…Very few blister test experiments have yet been reported for thin inorganic films on inorganic substrates [6] although bulge test is used for a long time for such systems [7][8][9][10][11][12][13]. In [4].…”

A two-step load-deflection procedure applicable to extract the Young's modulus and the residual tensile stress of circularly shaped thin-film diaphragms

“…Contrary to other closed-form relationships, which typically rely on one particular curvature characteristic (e.g., pure bending of ideal plates or membranes 51,53,54 ), this novel formula contains a set of parameters that can be chosen to describe all practically relevant bending curves. This enlarges significantly the number of different diaphragm types which can be studied.…”

“…The variety of utilized analytical methods spans approximate solutions of the nonlinear F€ oppl-von Karman equations, 3,49,50 Fourier expansions, 51 plain-strain relationships, 43,52 or energy methods. 53,54 Depending on the shape of the diaphragm, several models have been developed and published. Particularly, rectangular probes have been extensively studied 51,53,55,56 while circular diaphragms have been less frequently covered.…”

“…53,54 Depending on the shape of the diaphragm, several models have been developed and published. Particularly, rectangular probes have been extensively studied 51,53,55,56 while circular diaphragms have been less frequently covered. 54,57 Rectangular diaphragms with a high geometrical aspect ratio offer the advantage that the parameter extraction is less sensitive to uncertainties in the value of the Poisson's ratio.…”