  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.
