Micromechanical theory of strain-stiffening of biopolymer networks

TL;DR

This paper develops a theoretical and numerical framework to understand the strain-stiffening behavior of biopolymer networks, revealing critical properties of their nonlinear mechanical response.

Contribution

It introduces a simplified model and a comprehensive method to analyze the micro- and macro-mechanics of strain-stiffening biopolymer networks, advancing understanding of their nonlinear behavior.

Findings

Identifies the critical properties of strain-stiffening transition

Demonstrates the model's ability to replicate nonlinear stiffening behavior

Provides a robust numerical method for studying biopolymer mechanics

Abstract

Filamentous bio-materials such as fibrin or collagen networks exhibit an enormous stiffening of their elastic moduli upon large deformations. This pronounced nonlinear behavior stems from a significant separation between the stiffnesses scales associated with bending vs. stretching the material's constituent elements. Here we study a simple model of such materials - floppy networks of hinged rigid bars embedded in an elastic matrix - in which the effective ratio of bending to stretching stiffnesses vanishes identically. We introduce a theoretical framework and build upon it to construct a numerical method with which the model's micro- and macro-mechanics can be carefully studied. Our model, numerical method and theoretical framework allow us to robustly observe and fully understand the critical properties of the athermal strain-stiffening transition that underlies the nonlinear mechanical response of a broad class of biomaterials.