1
|
Amiri A, Duclut C, Jülicher F, Popović M. Random Traction Yielding Transition in Epithelial Tissues. PHYSICAL REVIEW LETTERS 2023; 131:188401. [PMID: 37977637 DOI: 10.1103/physrevlett.131.188401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 10/04/2023] [Indexed: 11/19/2023]
Abstract
We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude F_{c}. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.
Collapse
Affiliation(s)
- Aboutaleb Amiri
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Charlie Duclut
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Université Paris Cité, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, Paris, France
- Laboratoire Physico-Chimie Curie, CNRS UMR 168, Institut Curie, Université PSL, Sorbonne Université, 75005 Paris, France
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, Technical University of Dresden, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307 Dresden, Germany
| | - Marko Popović
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, Technical University of Dresden, 01307 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstrasse 108, 01307 Dresden, Germany
| |
Collapse
|
2
|
de Geus TWJ, Wyart M. Scaling theory for the statistics of slip at frictional interfaces. Phys Rev E 2022; 106:065001. [PMID: 36671104 DOI: 10.1103/physreve.106.065001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 10/07/2022] [Indexed: 06/17/2023]
Abstract
Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress σ^{*}, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a power law corresponding to "avalanches" and a "narrow" distribution of system-spanning "fracture" events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.
Collapse
Affiliation(s)
- T W J de Geus
- Physics Institute, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Matthieu Wyart
- Physics Institute, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|
3
|
Sastry S. Models for the Yielding Behavior of Amorphous Solids. PHYSICAL REVIEW LETTERS 2021; 126:255501. [PMID: 34241520 DOI: 10.1103/physrevlett.126.255501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 05/18/2021] [Indexed: 06/13/2023]
Abstract
Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behavior on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. Theoretical investigations of yielding in amorphous solids have almost exclusively focused on uniform deformation, but cyclic deformation reveals intriguing features that remain uninvestigated. Focusing on athermal cyclic deformation, I investigate a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy.
Collapse
Affiliation(s)
- Srikanth Sastry
- Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur Campus, Bengaluru 560064, India
| |
Collapse
|
4
|
Ferrero EE, Jagla EA. Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates. SOFT MATTER 2019; 15:9041-9055. [PMID: 31647078 DOI: 10.1039/c9sm01073d] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) ∼S-τSf(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃P(0) + xθ with P(0) ∼L-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent β ([small gamma, Greek, dot above]∼ (σ-σc)β) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.
Collapse
Affiliation(s)
- E E Ferrero
- Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina.
| | - E A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, Av. E. Bustillo 9500 (R8402AGP), San Carlos de Bariloche Río Negro, Argentina
| |
Collapse
|
5
|
de Geus TWJ, Popović M, Ji W, Rosso A, Wyart M. How collective asperity detachments nucleate slip at frictional interfaces. Proc Natl Acad Sci U S A 2019; 116:23977-23983. [PMID: 31699820 PMCID: PMC6883799 DOI: 10.1073/pnas.1906551116] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius [Formula: see text] governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding [Formula: see text] presents a pseudogap [Formula: see text], where θ is a nonuniversal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudogap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite-size effect, while the slip nucleation radius [Formula: see text] diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally.
Collapse
Affiliation(s)
- Tom W J de Geus
- Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;
| | - Marko Popović
- Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Wencheng Ji
- Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Alberto Rosso
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
| | - Matthieu Wyart
- Institute of Physics, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland;
| |
Collapse
|
6
|
Ferrero EE, Jagla EA. Elastic Interfaces on Disordered Substrates: From Mean-Field Depinning to Yielding. PHYSICAL REVIEW LETTERS 2019; 123:218002. [PMID: 31809180 DOI: 10.1103/physrevlett.123.218002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2019] [Indexed: 06/10/2023]
Abstract
We consider a model of an elastic manifold driven on a disordered energy landscape, with generalized long range elasticity. Varying the form of the elastic kernel by progressively allowing for the existence of zero modes, the model interpolates smoothly between mean-field depinning and finite dimensional yielding. We find that the critical exponents of the model change smoothly in this process. Also, we show that in all cases the Herschel-Buckley exponent of the flow curve depends on the analytical form of the microscopic pinning potential. Within the present elastoplastic description, all this suggests that yielding in finite dimensions is a mean-field transition.
Collapse
Affiliation(s)
- E E Ferrero
- Instituto de Nanociencia y Nanotecnología, CNEA-CONICET, Centro Atómico Bariloche, (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
| | - E A Jagla
- Centro Atómico Bariloche, Instituto Balseiro, Comisión Nacional de Energía Atómica, CNEA, CONICET, UNCUYO, Av. E. Bustillo 9500 (R8402AGP) San Carlos de Bariloche, Río Negro, Argentina
| |
Collapse
|
7
|
Fernández Aguirre I, Jagla EA. Critical exponents of the yielding transition of amorphous solids. Phys Rev E 2018; 98:013002. [PMID: 30110738 DOI: 10.1103/physreve.98.013002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Indexed: 06/08/2023]
Abstract
We investigate numerically the yielding transition of a two-dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, derived from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate versus stress curve, close to the critical stress, is of the form γ[over ̇]∼(σ-σ_{c})^{β}. Remarkably, we find that the value of β depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the β exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean-field version known as the Hébraud-Lequeux model.
Collapse
Affiliation(s)
- I Fernández Aguirre
- Comisión Nacional de Energía Atómica, Instituto Balseiro (UNCu), and CONICET Centro Atómico Bariloche, (8400) Bariloche, Argentina
| | - E A Jagla
- Comisión Nacional de Energía Atómica, Instituto Balseiro (UNCu), and CONICET Centro Atómico Bariloche, (8400) Bariloche, Argentina
| |
Collapse
|
8
|
Cao X, Nicolas A, Trimcev D, Rosso A. Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond? SOFT MATTER 2018; 14:3640-3651. [PMID: 29611574 DOI: 10.1039/c7sm02510f] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The deformation of disordered solids relies on swift and localised rearrangements of particles. The inspection of soft vibrational modes can help predict the locations of these rearrangements, while the strain that they actually redistribute mediates collective effects. Here, we study soft modes and strain redistribution in a two-dimensional continuous mesoscopic model based on a Ginzburg-Landau free energy for perfect solids, supplemented with a plastic disorder potential that accounts for shear softening and rearrangements. Regardless of the disorder strength, our numerical simulations show soft modes that are always sharply peaked at the softest point of the material (unlike what happens for the depinning of an elastic interface). Contrary to widespread views, the deformation halo around this peak does not always have a quadrupolar (Eshelby-like) shape. Instead, for finite and narrowly-distributed disorder, it looks like a fracture, with a strain field that concentrates along some easy directions. These findings are rationalised with analytical calculations in the case where the plastic disorder is confined to a point-like 'impurity'. In this case, we unveil a continuous family of elastic propagators, which are identical for the soft modes and for the equilibrium configurations. This family interpolates between the standard quadrupolar propagator and the fracture-like one as the anisotropy of the elastic medium is increased. Therefore, we expect to see a fracture-like propagator when extended regions on the brink of failure have already softened along the shear direction and thus rendered the material anisotropic, but not failed yet. We speculate that this might be the case in carefully aged glasses just before macroscopic failure.
Collapse
Affiliation(s)
- Xiangyu Cao
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris Saclay, Orsay, France.
| | | | | | | |
Collapse
|
9
|
Lin J, Wyart M. Microscopic processes controlling the Herschel-Bulkley exponent. Phys Rev E 2018; 97:012603. [PMID: 29448383 DOI: 10.1103/physreve.97.012603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2017] [Indexed: 06/08/2023]
Abstract
The flow curve of various yield stress materials is singular as the strain rate vanishes and can be characterized by the so-called Herschel-Bulkley exponent n=1/β. A mean-field approximation due to Hebraud and Lequeux (HL) assumes mechanical noise to be Gaussian and leads to β=2 in rather good agreement with observations. Here we prove that the improved mean-field model where the mechanical noise has fat tails instead leads to β=1 with logarithmic correction. This result supports that HL is not a suitable explanation for the value of β, which is instead significantly affected by finite-dimensional effects. From considerations on elastoplastic models and on the limitation of speed at which avalanches of plasticity can propagate, we argue that β=1+1/(d-d_{f}), where d_{f} is the fractal dimension of avalanches and d the spatial dimension. Measurements of d_{f} then supports that β≈2.1 and β≈1.7 in two and three dimensions, respectively. We discuss theoretical arguments leading to approximations of β in finite dimensions.
Collapse
Affiliation(s)
- Jie Lin
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Matthieu Wyart
- Institute of Theoretical Physics, Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| |
Collapse
|