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Register a new userRobust Prediction of Force Chains in Jammed Solids using Graph Neural Networks
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Force chains, which are quasi-linear self-organised structures carrying large stresses, are ubiquitous in jammed amorphous materials, such as granular materials, foams, emulsions or even assemblies of cells. Predicting where they will form upon mechanical deformation is crucial in order to describe the physical properties of such materials, but remains an open question. Here we demonstrate that graph neural networks (GNN) can accurately infer the location of these force chains in frictionless materials from the local structure prior to deformation, without receiving any information about the inter-particle forces. Once trained on a prototypical system, the GNN prediction accuracy proves to be robust to changes in packing fraction, mixture composition, amount of deformation, and the form of the interaction potential. The GNN is also scalable, as it can make predictions for systems much larger than those it was trained on. Our results and methodology will be of interest for experimental realizations of granular matter and jammed disordered systems, e.g. in cases where direct visualisation of force chains is not possible or contact forces cannot be measured.
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Using a system of repulsive, soft particles as a model for a jammed solid, we analyze its force network as characterized by the magnitude of the contact force between two particles, the local contact angle subtended between three particles, and the local coordination number. In particular, we measure the local contact angle distribution as a function of the magnitude of the local contact force. We find the suppression of small contact angles for locally larger contact forces, suggesting the existence of chain-like correlations in the locally larger contact forces. We couple this information with a coordination number-spin state mapping to arrive at a Potts spin model with frustration and correlated disorder to draw a potential connection between jammed solids (no quenched disorder) and spin glasses (quenched disorder). We use this connection to measure chaos due to marginality in the jammed system. In addition, we present the replica solution of the one-dimensional, long-range Potts glass as a potential toy building block for a jammed solid, where a sea of weakly interacting spins provide for long-range interactions along a chain-like backbone of more strongly interacting spins.
By calculating the linear response of packings of soft frictionless discs to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and non-affine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale $ell^*$ up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as $1/Delta z$, where $Delta z$ is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the non-affine displacements of the particles using the emph{displacement angle distribution}, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli.
The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the non-linear elastic exponent, the yielding strain/stress and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path towards understanding complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.
We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
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