Regeneration of surface roughness by the Langevin equation using stochastic analysis on AFM image of a carbon fiber

A new method was developed using AFM images of a fiber surface to regenerate the surface roughness in 3D geometry, such as the cylindrical shape of a “model” fiber. The Langevin equation was used to derive the fluctuations of a carbon fiber surface image. The equation contains two quantities, D(1) (h) and D(2) (h) which in physics represent drift and diffusion coefficients. Knowing this coefficient and adding a proper noise function, a similar surface of larger dimension with the same statistical properties of the initial data was created. The generated surface was mapped into cylindrical coordinates, then a mesh generated. The resulting reconstructed surface, input over the geometry of a cylindrical shape, can be implemented for finite element analysis of a single fiber surrounded by matrix and generalized to a many fiber model.