We construct a homogeneous, nonlinear elastic constitutive law, that modelsaspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers insuch networks buckle when in compression. We model this as a loss of stiffnessin compression in the stress-strain relations of the homogeneous constitutivemodel. Problems that model a contracting biological cell in a finite matrix aresolved. It is found that matrix displacements and stresses induced by cellcontraction decay slower (with distance from the cell) in a compressionweakening material, than linear elasticity would predict. This points toward amechanism for long-range cell mechanosensing. In contrast, an expanding cellwould induce displacements that decay faster than in a linear elastic matrix.
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