Abstract

A mathematical model has been developed for determining the geometric characteristics of porosity in deformable polymeric materials, using an optical fiber sensor with a distributed Bragg grating and based on the measurement of reflectance spectra that are part of the Fredholm integral equation of the first kind. The solution of this equation is the sought axial strain probability density function along the sensitive portion of the optical fiber with a Bragg grating. The results of a numerical simulation to obtain the geometric characteristics of porosity are presented: the relative volumetric concentration of spherical pores and the minimum guaranteed interlayer between pores located in a homogeneous elastic isotropic material under the influence of external hydrostatic stress. It was revealed that the porosity characteristics can be obtained from the density function of the strain distribution along the sensitive portion of the fiber with the Bragg grating, which was obtained from the solution of the Fredholm integral equation based on the measured spectra of reflection coefficients of the fiber optic sensor.

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