Criticality enhances the reinforcement of disordered networks by rigid inclusions
arXiv:2407.19563 · doi:10.1103/b9bh-rrj1
Abstract
The mechanical properties of biological materials are spatially heterogeneous. Typical tissues are made up of a spanning fibrous extracellular matrix in which various inclusions, such as living cells, are embedded. While the influence of inclusions on the stiffness of common elastic materials such as rubber has been studied for decades and can be understood in terms of the volume fraction and shape of inclusions, the same is not true for disordered filamentous and fibrous networks. Recent work has shown that, in isolation, such networks exhibit unusual viscoelastic behavior indicative of an underlying mechanical phase transition controlled by network connectivity and strain. How this behavior is modified when inclusions are present is unclear. Here, we present a theoretical and computational study of the influence of rigid inclusions on the mechanics of disordered elastic networks near the connectivity-controlled central force rigidity transition. Combining scaling theory and coarse-grained simulations, we predict and confirm an anomalously strong dependence of the composite stiffness on inclusion volume fraction, beyond that seen in ordinary composites. This stiffening exceeds the well-established volume fraction-dependent stiffening expected in conventional composites, e.g., as an elastic analogue of the classic volume fraction dependent increase in the viscosity of liquids first identified by Einstein. We show that this enhancement is a consequence of the interplay between inter-particle spacing and an emergent correlation length, leading to an effective finite-size scaling imposed by the presence of inclusions. We outline the expected scaling of the shear modulus and strain fluctuations with the inclusion volume fraction and network connectivity, confirm these predictions in simulations, and discuss potential experimental tests and implications for our predictions in real systems.
References in corpus (38)
- Nonlinear Elasticity in Biological Gels
- Elasticity of Semiflexible Biopolymer Networks
- Modeling semiflexible polymer networks
- Strain-induced alignment in collagen gels
- Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks
- Criticality and isostaticity in fiber networks
- Stiffening solids with liquid inclusions
- Long Range Force Transmission in Fibrous Matrices Enabled by Tension-Driven Alignment of Fibers
- Approximate analytical description of the nonaffine response of amorphous solids
- Biopolymers: life's mechanical scaffolds
- A coordination-based approach to elasticity of floppy and stiff random networks
- Strain-controlled criticality governs the nonlinear mechanics of fibre networks
- Finite-Size Scaling at the Jamming Transition
- Force-Extension Relation and Plateau Modulus for Wormlike Chains
- Elastic ripening and inhibition of liquid-liquid phase separation
- Floppy modes and non-affine deformations in random fiber networks
- Nonlinear effective medium theory of disordered spring networks
- Compression stiffening of fibrous networks with stiff inclusions
- Culinary fluid mechanics and other currents in food science
- Redundancy and cooperativity in the mechanics of compositely crosslinked filamentous networks
- The mechanical response of semiflexible networks to localized perturbations
- Actively stressed marginal networks
- Modelling Elastically-Mediated Liquid-Liquid Phase Separation
- Scaling theory for mechanical critical behavior in fiber networks
- Liquid demixing in elastic networks: cavitation, permeation, or size selection?
- Dynamical behavior of disordered spring networks
- Theory of elastic constants of athermal amorphous solids with internal stresses
- Micromechanical theory of strain-stiffening of biopolymer networks
- Stress-stabilized sub-isostatic fiber networks in a rope-like limit
- Loops versus lines and the compression stiffening of cells
- Finite size effects in critical fiber networks
- The Role of Cell-Matrix Interactions in Connective Tissue Mechanics
- Nonlinear Poisson effect governed by mechanical critical transition
- Thermoresponsive stiffening with microgel particles in a semiflexible fibrin network
- Theory of Elastic Microphase Separation
- Elasticity-Controlled Jamming Criticality in Soft Composite Solids
- Strain-controlled critical slowing down in the rheology of disordered networks
- Filled Colloidal Gel Rheology: Strengthening, Stiffening, and Tunability