A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells

TL;DR

This paper develops a nonlinear elastic model for fibrin networks that accounts for fiber buckling in compression, revealing how cell contraction influences long-range mechanical signaling in biological tissues.

Contribution

It introduces a novel constitutive law capturing compression-weakening behavior and analyzes the resulting elastic fields around contracting cells in such materials.

Findings

Displacements decay slower in compression-weakening materials, indicating long-range mechanosensing.

Expanding cells induce faster decay of displacements compared to linear elastic matrices.

Modeling explains biological phenomena of cell-matrix interactions and mechanotransduction.

Abstract

We construct a homogeneous, nonlinear elastic constitutive law, that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in compression in the stress-strain relations of the homogeneous constitutive model. Problems that model a contracting biological cell in a finite matrix are solved. It is found that matrix displacements and stresses induced by cell contraction decay slower (with distance from the cell) in a compression weakening material, than linear elasticity would predict. This points toward a mechanism for long-range cell mechanosensing. In contrast, an expanding cell would induce displacements that decay faster than in a linear elastic matrix.