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

摘要

Twisting and bending deformations are crucial to the biological functions ofmicrofilaments such as DNA molecules. Although continuum-rod models haveemerged as efficient tools to describe the nonlinear dynamics of thesedeformations, a major roadblock in the continuum-mechanics-based description ofmicrofilaments is the accurate modeling of the constitutive law, which followsfrom its atomistic structure and bond-stiffnesses. Since first-principlederivation of the constitutive law from atomistic structure is impractical andso are direct experimental measurements due to the small length-scales, anatural alternative is to estimate the constitutive law from discrete-structuresimulations such as molecular-dynamics (MD) simulations. In this paper, wepresent a two-step inverse method for estimating the constitutive law using rodtheory and data generated from discrete-structure simulations. We illustratethe method on a filament with an artificial and simplistic discrete-structure.We simulate its deformation in response to a prescribed loading using amulti-body dynamics (MBD) solver. Using data generated from the MBD solver, wefirst estimate the curvature of the filament and subsequently use it in thetwo-step method to estimate the effective constitutive-law relationship betweenthe restoring moment and curvature. Finally, we also illustrate how theestimated constitutive law can be tested under independent loading conditions.