A physically based approach to the accurate simulation of stiff fibers and stiff fiber meshes

We devise a physically based approach to the accurate simulation of stiff fibers like human hair, wool, or yarn. For that we describe fibers as three-dimensional coupled oscillator networks. The application of special analytical mapping expressions allows us to mimic the existence of Young's and shear modulus in the oscillator network so that real material parameters can be used. For the efficient numerical treatment of the stiff equations of motion of the system a Damped Exponential Time Integrator (DETI) is introduced. This type of integrator is able to take large time steps during the solution process of the stiff system while sustaining stability. It also handles Rayleigh damping analytically by employing the closed-form solution of the fully damped harmonic oscillator. We validate the fiber model against the outcome obtained by solving the special Cosserat theory of rods. Moreover, we demonstrate the efficiency of our approach on some complex fiber assemblies like human hair and fiber meshes. Compared to established methods we reach a significant speed up and at the same time achieve highly accurate results. Graphical abstractDisplay Omitted HighlightsWe devise a physically based approach to the accurate simulation of stiff fibers and fiber networks. For that, fibers are described as three-dimensional coupled oscillator networks because these are much easier to handle in complex contact situations than more strict continuum formulations like Cosserat rods. Also, we use special analytical expressions in order to admit the mapping of real values of Young's and shear modulus to the oscillator network and their spring constants, respectively.To evolve forward in time the stiff equations of motion of the fibers a Damped Exponential Time Integrator (DETI) is devised that is able to handle the stiff components of the equations of motion as well as Rayleigh damping fully analytically by employing the closed-form solution of the damped harmonic oscillator.This is accompanied by a thorough validation of the single fiber model against the Cosserat rod equations. We close with the presentation of convincing numerical examples as proof of concept.