Scaling laws for the response of nonlinear elastic media with implications for cell mechanics

Abstract

We show how strain stiffening affects the elastic response to internal forces, caused either by material defects and inhomogeneities or by active forces that molecular motors generate in living cells. For a spherical force dipole in a material with a strongly nonlinear strain energy density, strains change sign with distance, indicating that even around a contractile inclusion or molecular motor there is radial compression; it is only at long distance that one recovers the linear response in which the medium is radially stretched. Scaling laws with irrational exponents relate the far-field renormalized strain to the near-field strain applied by the inclusion or active force.

4 pages, 3 figures, accepted to Physical Review Letters

References in corpus (7)

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• Strain-induced alignment in collagen gels
• A master relation defines the nonlinear viscoelasticity of single fibroblasts
• Elastic Interactions of Cells
• Elastic interactions of active cells with soft materials
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• Continuum elastic models for force transmissions in biopolymer gels
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• Anomalous linear elasticity of disordered networks
• Modeling Multi-Cellular Dynamics Regulated by ECM-Mediated Mechanical Communication via Active Particles with Polarized Effective Attraction
• Mean-field interactions between living cells in linear and nonlinear elastic matrices
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• Collective dynamics and self-organization of active particles on random networks