prof.dr. Prashant Purohit: Stiffening, softening and collapse in filament networks

Abstract

A new method of combining structural and statistical mechanics is presented in order to study the entropic elasticity of semi flexible filament networks. We view a filament network as a frame structure and use structural mechanics to determine its static equilibrium configuration under applied loads in the first step. To account for thermal motion around this static equilibrium state, we then approximate the potential energy of the deformed frame structure up to the second order in kinematic variables and obtain a deformation-dependent stiffness matrix characterizing the flexibility of the network.
Using statistical mechanics, we then evaluate the partition function, free energy and thermo-mechanical properties of the network in terms of the stiffness matrix.
Using our method we are able to capture the stress-stiffening behavior due to filament reorientation and stretching out of thermal fluctuations, as well as the reversible stress-softening behavior due to filament buckling.

In a separate study combining finite elements with Kinetic Monte Carlo techniques we explore the rate-dependent elasticity and softening due to damage in biofilament networks. As part of this study we also present a continuum model to account for the damage evolution in filament network.