Highly Sensitive and Durable Structured Fibre Sensors for Low-Pressure Measurement in Smart Skin

Precise measurements of low pressure are highly necessary for many applications. This study developed novel structured fibre sensors embedded in silicone, forming smart skin with high sensitivity, high durability, and good immunity to crosstalk for precise measurement of pressure below 10 kPa. The transduction principle is that an applied pressure leads to bending and stretching of silicone and optical fibre over a purposely made groove and induces the axial strain in the gratings. The fabricated sensor showed high pressure sensitivity up to 26.8 pm/kPa and experienced over 1,000,000 cycles compression without obvious variation. A theoretical model of the sensor was presented and verified to have excellent agreement with experimental results. The prototype of smart leg mannequin and wrist pulse measurements indicated that such optical sensors can precisely measure low-pressure and can easily be integrated for smart skins for mapping low pressure on three-dimensional surfaces.


S1. Theoretical treatment of structured fibre pressure sensor
The designed sensor shown in Figure 1a is comprising by matrix, optical fibre with fibre Bragg gratings, a spacer, and a rigid base with a rectangular groove. First, only mall deformation of all components occurs due to the fracture strain of silica is only 0.6% [1]. Accordingly, it is reasonable to assume that all components are made by the linear-elastic material. Secondly, the optical fibre is well fixed on the rigid base by using glues (Aron alpha). The stiffness of the base made of ABS or Invar are three orders higher than that of optical fibre or the silicone film. Coupled with the above announcements, the fixed optical fibre can be considered as an elastic beam with the built-in condition. Thirdly, the film over the groove is simplified as a simplysupported plate. Because only part of bottom surface of the film is fixed on the base, while the top surface of the film is free. Moreover, the thin film is normally soft and has very low elastic modulus comparing to that of the base. For those reasons, the thin film can be simplified as a simply-supported plate. Fourthly, the groove has a sufficient depth, so that the optical fibre will not touch the bottom of the groove during deformation. Fifthly, the influences of the spacer on the flexural stiffness on the optical fibre and the soft matrix film are neglected. As well as the deformation of spacer in the compression direction is also neglected. Moreover, the spacer has a sufficient thickness, so that the optical fibre does not contact with the thin film on the zone over 2 the groove. Sixthly, the wavelength of FBGs induced by the pressure applied from the spacer can be neglected comparing to that inducing by axial deformation. To construct the theoretical model, several assumptions are made. From these assumptions, three cases will be included: a simply-supported rectangular plate with a load uniformly distributed over a rectangle zone shown in Figure 1b, which is corresponding to the shape of the spacer, a simply-supported rectangular plate under a uniform pressure shown in Figure 1c, and a built-in beam under a uniform load over the center part shown in Figure 1d, corresponding to the length of the spacer.

S1.1 Theoretical Treatments of a Simply-Supported Plate under Uniform Pressure
Let us firstly consider the case of a simply-supported rectangular plate under a uniform load, p1, distributed over a shaded rectangle (corresponding to the spacer) with the sides of as and bs, shown in Figure 1b. The derivation of deflection, W1, is similar to that shown in reference [2]  Similarly, as shown in Figure 1c, a uniform load, p, is distributed over the whole rectangle, meaning s aa  and s bb  , thus, the deflection,W2, at any point of the plate can be given by

S1.2. Theoretical Treatments of a Built-in Beam under a Load Uniformly Distributed at the Center Part
As shown in Figure 1d, a load, q, is uniformly distributed at the center part of a built- where the arbitrary constant C0 is the moment at the center of the beam.
Finally, the deflection can be given by the integration of the shear and moment. (S1-10)

S1.3. Evaluation of Average Axial Strain of the Built-in Beam
After fabrication, the plate and the beam have an initial deflection due to a spacer is setup between the plate and the beam. At the initial condition,