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.
@article{arxiv.1412.2612,
title = {A Model for Compression-Weakening Materials and the Elastic Fields due to Contractile Cells},
author = {Phoebus Rosakis and Jacob Notbohm and Guruswami Ravichandran},
journal= {arXiv preprint arXiv:1412.2612},
year = {2015}
}