Modeling and analysis of the effect of strain gradient to design diaphragm for pressure sensing application through finite element analysis

Capacitive and optical-based pressure sensors are considered for wide application in industries and R&D labs due to their superior performance. In general, these sensors use a diaphragm as a sensing element that needs to be designed accurately to achieve the desired level of accuracy for a higher operating range of the sensor. To design such a diaphragm, the conventional strain-based model cannot be used efficiently as the strain gradient starts dominating to introduce non-linear deformation with respect to the applied load when the diaphragm thickness reduces or the operating range increases beyond a certain value. Thus, there is a need to establish a comprehensive understanding and accurate modeling method to establish the underlying mechanism of the strain gradient. In view of this, a finite element analysis is carried out with moving-mesh to investigate the effect of the strain gradient phenomenon extensively in this paper. For the investigation, a few parameters are studied such as strain, strain gradient, bending rigidity, and deflection. It shows that the strain gradient spreads radially on the diaphragm and its zone of influence depends on the thickness as well as the applied pressure. This increases the bending rigidity significantly and the diaphragm deflection becomes non-linear as compared to the classical theory of bending. For validation of the present model, the bending rigidity and the deflection behavior are also compared with an earlier developed mathematical model as well as experimental results, and the same is discussed in this paper. The present work is useful for an accurate design and optimization of a diaphragm or a flexure for small size or/and higher operating range of pressure sensors and actuators.