Constitutive-Law Modeling of Microfilaments From Their Discrete-Structure Simulations—A Method Based on an Inverse Approach Applied to a Static Rod Model

Abstract

Twisting and bending deformations are crucial to the biological functions of several microfilaments such as DNA molecules. Although continuum-rod models have emerged as efficient tools to describe the nonlinear dynamics of these deformations, a major roadblock in the continuum–mechanics-based description of microfilaments is the accurate modeling of the constitutive law, which follows from their atomistic-level structure and interactions. In this paper, we present a method for estimating the constitutive law using a static rod model and deformed configuration data generated from discrete-structure simulations. Furthermore, we illustrate the method on a filament with an artificial discrete-structure. We simulate its deformation in response to a prescribed loading using a multibody dynamics (MBD) solver. Using position data generated from the MBD solver, we first estimate the curvature of the filament, and subsequently use it to estimate the effective relationship between the restoring moment and curvature.