A model for compression-weakening materials and the elastic fields due to contractile cells
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.
Additional Information© 2015 Elsevier Ltd. Received 4 May 2015, Revised 7 August 2015, Accepted 25 August 2015, Available online 2 September 2015. This work was motivated by experiments performed in collaboration with Dr. Ayelet Lesman and Professor David Tirrell under a grant from the National Science Foundation (Division of Materials Research No. 0520565) through the Center for the Science and Engineering of Materials at the California Institute of Technology. P.R. acknowledges the hospitality of the Graduate Aerospace Laboratories at the California Institute of Technology (GALCIT).
Submitted - 1412.2612v3.pdf