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

TL;DR

This paper introduces a two-step inverse method to derive constitutive laws for microfilaments from discrete-structure simulations, enabling continuum models to accurately reflect atomistic behaviors without direct experimental measurements.

Contribution

It presents a novel inverse approach combining rod theory and simulation data to estimate constitutive laws from discrete microstructure models.

Findings

Successfully estimated constitutive law from simulation data

Validated the method with independent loading tests

Provided a framework for linking atomistic simulations to continuum models

Abstract

Twisting and bending deformations are crucial to the biological functions of 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 structure and bond-stiffnesses. Since first-principle derivation of the constitutive law from atomistic structure is 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 present a two-step inverse method for estimating the constitutive law using rod theory and data generated from discrete-structure simulations. We illustrate the method on a filament with an artificial and simplistic discrete-structure. We simulate its deformation in response to a prescribed loading using a multi-body dynamics (MBD) solver. Using data generated from the MBD solver, we first estimate the curvature of the filament and subsequently use it in the two-step 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 tested under independent loading conditions.