arXiv subjects

Suzanne M. Fielding

Publications and source records attributed to Suzanne M. Fielding.

At least 19 recordsLinked to original sources

arXiv2026

Viscoelasticity and elastoplasticity in the power law creep and yielding of gels and fibre network materials under stress

We study computationally the creep and yielding of athermal gels and fibre network materials under a constant imposed shear stress, within a minimal model of interconnected filaments with central forces in $d=2$ spatial dimensions. Each filament is assumed Hookean initially, then breaks irreversibly above a threshold strain. At early times after the imposition of a small stress, we find purely viscoelastic creep response associated with non-affine deformations within the material, with solid terminal behaviour for a network coordination $Z>2d=4$ and initially floppy response for $Z<4$. For a marginally connected network, $Z=4$, we find sustained power law creep with a strain rate $\dotγ\sim t^{-1/2}$ and strain $γ\sim t^{1/2}$ as a function of time $t$ after the imposition of the stress. This viscoelastic regime gives way at later times to elastoplastic creep arising from filament breakage, broadening the range of values of $Z$ and time over which power law creep occurs, compared to a network with filament breakage disallowed. This accumulating filament breakage can weaken the network to such an extent that catastrophic material failure then occurs after a long delay, which we characterise. Finally, we consider the implications of viscoelastic versus elastoplastic deformation for the extent to which a material will recover its original shape if the load is removed after some interval of creep.

cond-mat.soft↗

arXiv2026

Fluid-Solid Pattern Formation and Strain Localisation via Shear Banding Instability in Model Biological Tissues

The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of spatial patterns. Dating back to Turing, pattern formation has been suggested to arise in tissues via spontaneous symmetry breaking instabilities in the concentration field of chemical morphogens. Within the vertex model of tissue mechanics, we show that spontaneous symmetry breaking may also arise via a mechanical instability in the strain field of a deformed tissue, leading to a patterned coexistence of fluid and solid regions, with a strong localisation of the strain into shear bands. The nature of the bands differs between tissues in which internal cell-cell dissipation dominates external drag against a substrate, and vice versa.

cond-mat.soft↗

arXiv2026

Elastic turbulence in highly entangled polymers and wormlike micelles

We show theoretically that an initially homogeneous planar Couette flow of a concentrated polymeric fluid is linearly unstable to the growth of two-dimensional (2D) perturbations, within two widely used constitutive models: the Johnson-Segalman model and the Rolie-Poly model. We perform direct nonlinear simulations of both models in 2D to show that this instability leads to a state of elastic turbulence comprising several narrow shear bands that dynamically coalesce, split and interact. Importantly, we show that this 2D instability arises not only in fluids that have a non-monotonic constitutive curve, and therefore show shear banding in 1D calculations, but also in shear thinning fluids with a monotonic constitutive curve, for which an initially homogeneous base state is stable in 1D. For the former category, the high shear branch of the constitutive curve is unstable to 2D instability in both models, so that the high shear band may be turbulent. In the Rolie-Poly model, the low shear branch is also likewise unstable. Our work provides the first simulation evidence for elastic turbulence in highly entangled polymeric fluids. It also potentially explains rheo-chaotic states seen experimentally in shear banding wormlike micelles. We additionally demonstrate elastic turbulence within both models in the planar Poiseuille geometry.

cond-mat.soft↗

arXiv2025

Toughness of double network hydrogels: the role of reduced stress propagation

Double network hydrogels show remarkable mechanical performance, combining high strength and fracture toughness with sufficient stiffness to bear load, despite containing only a low density of cross-linked polymer molecules in water. We introduce a simple mesoscale model of a double network material, detailed enough to resolve the salient microphysics of local plastic bond breakage, yet simple enough to address macroscopic cracking. Load sharing between the networks results in a delocalisation of stress such that the double network inherits both the stiffness of its stiff-and-brittle sacrificial network and the ductility of its soft-and-ductile matrix network. The underlying mechanism is a reduction in the Eshelby stress propagator between sacrificial bonds, inhibiting the tendency for the plastic failure of one sacrificial bond to propagate stress to neighbouring sacrificial bonds and cause a follow-on cascade of breakages. The mechanism of brittle macroscopic cracking is thereby suppressed, giving instead ductile deformation via diffusely distributed microcracking.

cond-mat.soft↗

arXiv2025

Ultra-delayed material failure via shear banding after straining an amorphous material

We predict a phenomenon of catastrophic material failure arising suddenly within an amorphous material, with an extremely long delay time since the material was last deformed. By simulating a mesoscopic soft glassy rheology model in one dimension (1D), a mesoscopic elastoplastic model in 1D and 2D, and a continuum fluidity model in 1D, we demonstrate the basic physics to involve a dramatic ultra-delayed shear banding instability, in which strain suddenly strongly localises within the material and the stress drops precipitously. The delay time after the long historical shear strain was applied before failure occurs increases steeply with decreasing strain amplitude, decreasing working temperature, and increasing sample annealing prior to shear. In demonstrating the same physics -- which is directly testable experimentally and in particle simulations -- to obtain within three different constitutive models, we suggest it may be generic across amorphous materials. The counter-intuitive prediction of catastrophic material failure long after any deformation was last applied could have important consequences for material processing and performance.

cond-mat.soft↗

arXiv2025

Recoverable strain in amorphous materials: the role of ongoing plastic events following initial elastic recoil

Recoverable strain is the strain recovered once a stress is removed from a body, in the direction opposite to that in which the stress had acted. To date, the phenomenon has been understood as being elastic in origin: polymer chains stretched in the direction of an imposed stress will recoil after the stress is removed, for example. Any unrecoverable strain is instead attributed to irreversible plastic deformations. Here we study theoretically strain recovery within the soft glassy rheology model, aimed at describing the rheology of elastoplastic yield stress fluids and amorphous soft solids. We consider a material subject to the switch-on of a shear stress that is held constant before later being set back to zero, after which the strain recovery is observed. After an initially fast recoil that is indeed elastic in nature, significant further strain recovery then occurs more slowly via the plastic yielding of elements with negative local stresses, opposite to that of the original shear. We elucidate the mechanism that underlies this behaviour, in terms of the evolution of the SGR model's population of elastoplastic elements. In particular, we show that the initial fast elastic recoil brings to a state of negative local stress those elements that had yielded during the forward straining while the load was applied. The subsequent delayed plastic yielding of these elements with negative stress is the origin of the slow ongoing strain recovery. In this way, counterintuitively, elements that had yielded plastically while the load was applied still contribute significantly to strain recovery after the sample is unloaded. This finding has important consequences for constitutive modeling, because such behaviour can only arise in a constitutive model that evolves a full distribution of local stresses (or multiple moments of such a distribution), rather than a single average stress.

cond-mat.soft↗

arXiv2025

Shear banding as a cause of non-monotonic stress relaxation after flow cessation

Recent flow cessation experiments on soft materials have shown a counter-intuitive non-monotonic relaxation of the shear stress: following the switch-off of a steady imposed shear flow, the stress initially decays before later increasing again. By simulating the soft glassy rheology model in a form extended to allow steady state shear banding, we show that the presence of shear bands prior to flow cessation can give rise to this phenomenon. We give a mechanistic understanding of the basic physics involved, in terms of (i) the decay of the shear bands after flow cessation, and (ii) the evolution of frustrated local stresses, governed by different time scales for plastic relaxation in each band. In particular, an elastic recoil in the unsheared band gives rise to negative local frustrated stresses, the slow release of which can cause an increase in macroscopic stress. Given that shear banding and frustrated local stresses arise widely across disordered soft solids, we argue that non-monotonic stress relaxation after flow cessation may occur in many different materials.

cond-mat.soft↗

arXiv2025

Non-monotonic constitutive curves and shear banding in dry and wet granular flows

We use particle simulations to map comprehensively the shear rheology of dry and wet granular matter comprising particles of finite stiffness, in both fixed pressure and fixed volume protocols. At fixed pressure we find non-monotonic constitutive curves that are shear thinning, whereas at fixed volume we find non-monotonic constitutive curves that are shear thickening. We show that the presence of one non-monotonicity does not imply the other. Instead, there exists a signature in the volume fraction measured under fixed pressure that, when present, ensures non-monotonic constitutive curves at fixed volume. In the context of dry granular flow we show that gradient and vorticity bands arise under fixed pressure and volume respectively, as implied by the constitutive curves. For wet systems our results are consistent with a recent experimental observation of shear thinning at fixed pressure. We furthermore predict discontinuous shear thickening in the absence of critical load friction.

cond-mat.soft↗

arXiv2024

Simple and effective mechanical cloaking

We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a homogeneous isotropic linear elastic material of prescribed shear modulus. Importantly, we find that the same combination of annuli will cloak any possible mode of imposed deformation or loading, for any randomly chosen admixture of imposed compression, pure shear and simple shear, without the need to re-design the cloak for different deformation modes. A full range of circular inclusions can be cloaked in this way, from soft to stiff. In consequence, we suggest that an inclusion of any arbitrary shape can also be cloaked, by first enveloping it in a stiff circle, then cloaking the combined structure with three annuli as described. Given that a single inclusion can be fully cloaked in this way, even at near field close to the cloaking perimeter, it also follows that multiple such neutral inclusions arranged with arbitrarily high packing fraction in a surrounding medium can also be cloaked. We confirm this by direct simulation. This indicates a possible route to fabricating composite materials with the same global mechanical response as a counterpart homogeneous material, and with uniform strain and stress fields outwith the cloaked inclusions.

cond-mat.soft↗

arXiv2024

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials

Materials with negative Poisson ratio have the counter-intuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localised plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighbouring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

cond-mat.stat-mech↗

arXiv2024

Slow fatigue and highly delayed yielding via shear banding in oscillatory shear

We study theoretically the dynamical process of yielding in cyclically sheared amorphous materials, within a thermal elastoplastic model and the soft glassy rheology model. Within both models we find an initially slow accumulation, over many cycles after the inception of shear, of low levels of damage in the form strain heterogeneity across the sample. This slow fatigue then suddenly gives way to catastrophic yielding and material failure. Strong strain localisation in the form of shear banding is key to the failure mechanism. We characterise in detail the dependence of the number of cycles N* before failure on the amplitude of imposed strain, the working temperature, and the degree to which the sample is annealed prior to shear. We discuss our finding with reference to existing experiments and particle simulations, and suggest new ones to test our predictions.

cond-mat.soft↗

arXiv2024

Power law creep and delayed failure of gels and fibrous materials under stress

Motivated by recent experiments studying the creep and breakup of a protein gel under stress, we introduce a simple mesoscopic model for the irreversible failure of gels and fibrous materials, and demonstrate it to capture much of the phenomenology seen experimentally. This includes a primary creep regime in which the shear rate decreases as a power law over several decades of time, a secondary crossover regime in which the shear rate attains a minimum, and a tertiary regime in which the shear rate increases dramatically up to a finite time singularity, signifying irreversible material failure. The model also captures a linear Monkman-Grant scaling of the failure time with the earlier time at which the shear rate attained its minimum, and a Basquin-like power law scaling of the failure time with imposed stress, as seen experimentally. The model furthermore predicts a slow accumulation of low levels of material damage during primary creep, followed by the growth of fractures leading to sudden material failure, as seen experimentally.

cond-mat.soft↗

arXiv2024

Discontinuous shear thickening in biological tissue rheology

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate in particular the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming/unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening (CST) and discontinuous shear thickening (DST). These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors {\it in vivo}.

cond-mat.soft↗

arXiv2023

Constitutive model for the rheology of biological tissue

The rheology of biological tissue is key to processes such as embryo development, wound healing and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquid-like tissue. Alongside this jamming/unjamming behaviour, biological tissue also displays an inherent viscoelasticity, with a slow time and rate dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.

cond-mat.soft↗

arXiv2022

Shear-driven solidification and nonlinear elasticity in epithelial tissues

Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity observed in other soft matter systems. Interestingly, shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order critical point that governs the liquid-solid transition of the undeformed system. We further show that a solidlike tissue responds linearly only to small strains and but then switches to a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.

cond-mat.soft↗

arXiv2021

Perspectives on viscoelastic flow instabilities and elastic turbulence

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences.

physics.flu-dyn↗

arXiv2021

Power fluctuations in sheared amorphous materials: A minimal model

The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical micro-rheological experiments.

cond-mat.soft↗

arXiv2021

Wall slip and bulk yielding in soft particle suspensions

We simulate a dense athermal suspension of soft particles sheared between hard walls of a prescribed roughness profile, using a method that fully accounts for the fluid mechanics of the solvent between the particles, and between the particles and the walls, as well as for the solid mechanics of changes in the particle shapes. We thus capture the widely observed phenomenon of elastohydrodynamic wall slip, in which the soft particles become deformed in shear and lift away from the wall slightly, leaving behind a thin lubricating solvent layer of high shear. For imposed stresses below the material's bulk yield stress, we show the observed wall slip to be dominated by this thin solvent layer. At higher stresses, it is augmented by an additional contribution arising from a fluidisation of the first few layers of particles near the wall. By systematically varying the roughness of the walls, we quantify a suppression of slip with increasing wall roughness. For smooth walls, slip radically changes the steady state bulk flow curve of shear stress as a function of shear rate, by conferring a branch of apparent (slip-induced) flow even for $σ<σ_y$, as seen experimentally. We also elucidate the effects of slip on the dynamics of yielding following the imposition of a constant shear stress, characterising the timescales at which bulk yielding arises, and at which slip first sets in.

cond-mat.soft↗