Constitutive-law Modeling of Microfilaments from their Discrete-Structure Simulations - A Method based on an Inverse Approach Applied to a Static Rod Model

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 its atomistic-level structure and interactions. Since firstprinciple derivation of the constitutive law from atomistic-level structure and interactions is often impractical and so are direct experimental measurements due to the small length-scales, a natural alternative is to estimate the constitutive law from discrete-structure simulations such as molecular-dynamics (MD) simulations. In this paper, we describe a method based on a recently proposed two-step inverse approach [1] for estimating the constitutive law Preprint submitted to ASME Journal of Applied Mechanics December 3, 2010 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 multi-body dynamics (MBD) solver, Hyperworks MotionView. Using position data generated from the MBD solver, we first estimate the curvature of the filament, and subsequently use it in the described method to estimate the effective constitutive-law relationship between the restoring moment and curvature. Finally, we also illustrate how the estimated constitutive law can be validated under independent loading conditions.