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

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.

18 pages, 2 figures

References in corpus (5)

• Stress controls the mechanics of collagen networks
• Long Range Force Transmission in Fibrous Matrices Enabled by Tension-Driven Alignment of Fibers
• Microbuckling of Fibrin Provides a Mechanism for Cell Mechanosensing
• Crosslinked networks of stiff filaments exhibit negative normal stress
• Scaling laws for the response of nonlinear elastic media with implications for cell mechanics

Cited by in corpus (12)

• Cell contraction induces long-ranged stress stiffening in the extracellular matrix
• Fiber networks amplify active stress
• Nonlinear elasticity of the extracellular matrix fibers facilitates efficient inter-cellular mechanical communication
• Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix
• Shape regulation generates elastic interaction between living cells
• Continuum elastic models for force transmissions in biopolymer gels
• Fiber plucking by molecular motors yields large emergent contractility in stiff biopolymer networks
• Active gels, heavy tails, and the cytoskeleton
• Geometry underlies the mechanical stiffening and softening of an indented floating film
• Programming filamentous network mechanics by compression
• Geometry-Driven Mechanical Memory in a Random Fibrous Matrix
• Elastic Anisotropy Governs the Decay of Cell-induced Displacements