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Kamani KM, Rogers SA. Brittle and ductile yielding in soft materials. Proc Natl Acad Sci U S A 2024; 121:e2401409121. [PMID: 38776367 PMCID: PMC11145261 DOI: 10.1073/pnas.2401409121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2024] [Accepted: 04/29/2024] [Indexed: 05/25/2024] Open
Abstract
Many soft materials yield under mechanical loading, but how this transition from solid-like behavior to liquid-like behavior occurs can vary significantly. Understanding the physics of yielding is of great interest for the behavior of biological, environmental, and industrial materials, including those used as inks in additive manufacturing and muds and soils. For some materials, the yielding transition is gradual, while others yield abruptly. We refer to these behaviors as being ductile and brittle. The key rheological signatures of brittle yielding include a stress overshoot in steady-shear-startup tests and a steep increase in the loss modulus during oscillatory amplitude sweeps. In this work, we show how this spectrum of yielding behaviors may be accounted for in a continuum model for yield stress materials by introducing a parameter we call the brittility factor. Physically, an increased brittility decreases the contribution of recoverable deformation to plastic deformation, which impacts the rate at which yielding occurs. The model predictions are successfully compared to results of different rheological protocols from a number of real yield stress fluids with different microstructures, indicating the general applicability of the phenomenon of brittility. Our study shows that the brittility of soft materials plays a critical role in determining the rate of the yielding transition and provides a simple tool for understanding its effects under various loading conditions.
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Affiliation(s)
- Krutarth M. Kamani
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Champaign, IL61801
| | - Simon A. Rogers
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Champaign, IL61801
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Cochran JO, Callaghan GL, Caven MJG, Fielding SM. Slow Fatigue and Highly Delayed Yielding via Shear Banding in Oscillatory Shear. PHYSICAL REVIEW LETTERS 2024; 132:168202. [PMID: 38701472 DOI: 10.1103/physrevlett.132.168202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2022] [Revised: 11/21/2023] [Accepted: 03/15/2024] [Indexed: 05/05/2024]
Abstract
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 localization in the form of shear banding is key to the failure mechanism. We characterize 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.
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Affiliation(s)
- James O Cochran
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Grace L Callaghan
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Miles J G Caven
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
| | - Suzanne M Fielding
- Department of Physics, Durham University, Science Laboratories, South Road, Durham DH1 3LE, United Kingdom
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Aufderhorst-Roberts A, Cussons S, Brockwell DJ, Dougan L. Diversity of viscoelastic properties of an engineered muscle-inspired protein hydrogel. SOFT MATTER 2023; 19:3167-3178. [PMID: 37067782 DOI: 10.1039/d2sm01225a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
Folded protein hydrogels are prime candidates as tuneable biomaterials but it is unclear to what extent their mechanical properties have mesoscopic, as opposed to molecular origins. To address this, we probe hydrogels inspired by the muscle protein titin and engineered to the polyprotein I275, using a multimodal rheology approach. Across multiple protocols, the hydrogels consistently exhibit power-law viscoelasticity in the linear viscoelastic regime with an exponent β = 0.03, suggesting a dense fractal meso-structure, with predicted fractal dimension df = 2.48. In the nonlinear viscoelastic regime, the hydrogel undergoes stiffening and energy dissipation, indicating simultaneous alignment and unfolding of the folded proteins on the nanoscale. Remarkably, this behaviour is highly reversible, as the value of β, df and the viscoelastic moduli return to their equilibrium value, even after multiple cycles of deformation. This highlights a previously unrevealed diversity of viscoelastic properties that originate on both at the nanoscale and the mesoscopic scale, providing powerful opportunities for engineering novel biomaterials.
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Affiliation(s)
- Anders Aufderhorst-Roberts
- Department of Physics, Centre for Materials Physics, University of Durham, Durham, DH1 3LE, UK
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK.
| | - Sophie Cussons
- Astbury Centre for Structural Molecular Biology, University of Leeds, Leeds, UK
- School of Molecular and Cellular Biology, Faculty of Biological Sciences, University of Leeds, Leeds, LS2 9JT, UK
| | - David J Brockwell
- Astbury Centre for Structural Molecular Biology, University of Leeds, Leeds, UK
- School of Molecular and Cellular Biology, Faculty of Biological Sciences, University of Leeds, Leeds, LS2 9JT, UK
| | - Lorna Dougan
- School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK.
- Astbury Centre for Structural Molecular Biology, University of Leeds, Leeds, UK
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Cho JH, Bischofberger I. Yield precursor in primary creep of colloidal gels. SOFT MATTER 2022; 18:7612-7620. [PMID: 36165999 DOI: 10.1039/d2sm00884j] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Colloidal gels under constant moderate stress flow only after a prolonged solid-like deformation. Predicting the time-dependent yielding of the gels would facilitate control of their mechanical stability and transport, but early detectable signs of such delayed solid-to-fluid transition remain unknown. We show that the shear rate of colloidal gels under constant stress can forecast an eventual yielding during the earliest stage of deformation known as primary creep. The shear rate before failure exhibits a characteristic power-law decrease as a function of time, distinct from the linear viscoelastic response. We model this early-stage behavior as a series of uncorrelated local plastic events that are thermally activated, which illuminates the exponential dependence of the yield time on the applied stress. By revealing underlying viscoplasticity, this precursor to yield in the macroscopic shear rate provides a convenient tool to predict the yielding of a gel well in advance of its actual occurrence.
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Affiliation(s)
- Jae Hyung Cho
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
| | - Irmgard Bischofberger
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
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Martin AJ, Li W, Watts J, Hilmas GE, Leu MC, Huang T. Particle Migration in Large Cross-Section Ceramic On-Demand Extrusion Components. Ann Ital Chir 2022. [DOI: 10.1016/j.jeurceramsoc.2022.10.059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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Tauber J, van der Gucht J, Dussi S. Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations. J Chem Phys 2022; 156:160901. [PMID: 35490006 DOI: 10.1063/5.0081316] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.
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Affiliation(s)
- Justin Tauber
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
| | - Simone Dussi
- Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands
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Griffiths SE, Koumakis N, Brown AT, Vissers T, Warren PB, Poon WCK. Diffusion, phase behavior, and gelation in a two-dimensional layer of colloids in osmotic equilibrium with a polymer reservoir. J Chem Phys 2021; 155:074903. [PMID: 34418940 DOI: 10.1063/5.0058172] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The addition of enough non-adsorbing polymers to an otherwise stable colloidal suspension gives rise to a variety of phase behaviors and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a study of these phenomena in a two-dimensional layer of colloids. The three-dimensional phenomenology of crystal-fluid coexistence is reproduced, but gelation takes a novel form, in which the strands in the gel structure are locally crystalline. We compare our findings with a previous simulation and theory and find substantial agreement.
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Affiliation(s)
- Sam E Griffiths
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Nick Koumakis
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Aidan T Brown
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Teun Vissers
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
| | - Patrick B Warren
- Hartree Centre, Science and Technology Facilities Council (STFC), Sci-Tech Daresbury, Warrington WA4 4AD, United Kingdom
| | - Wilson C K Poon
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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Abstract
Machine learning is making a major impact in materials research. I review current progress across a selection of areas of ubiquitous soft matter. When applied to particle tracking, machine learning using convolution neural networks is providing impressive performance but there remain some significant problems to solve. Characterising ordered arrangements of particles is a huge challenge and machine learning has been deployed to create the description, perform the classification and tease out an interpretation using a wide array of techniques often with good success. In glass research, machine learning has proved decisive in quantifying very subtle correlations between the local structure around a site and the susceptibility towards a rearrangement event at that site. There are also beginning to be some impressive attempts to deploy machine learning in the design of composite soft materials. The discovery aspect of this new materials design meets the current interest in teaching algorithms to learn to extrapolate beyond the training data.
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Affiliation(s)
- Paul S Clegg
- School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, UK.
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Liu C, Dutta S, Chaudhuri P, Martens K. Elastoplastic Approach Based on Microscopic Insights for the Steady State and Transient Dynamics of Sheared Disordered Solids. PHYSICAL REVIEW LETTERS 2021; 126:138005. [PMID: 33861121 DOI: 10.1103/physrevlett.126.138005] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2020] [Accepted: 02/26/2021] [Indexed: 06/12/2023]
Abstract
We develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse-grained quantities from simulations of dense disordered particulate systems, we present a coherent elastoplastic model approach for deformation and flow of yield stress materials. For a given set of parameters, this model allows us to match consistently transient and steady state features of driven disordered systems with diverse preparation histories under both applied shear-rate and creep protocols.
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Affiliation(s)
- Chen Liu
- Laboratoire de Physique de l'Ecole Normale Suprieure, 75005 Paris, France
| | - Suman Dutta
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
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Pommella A, Cipelletti L, Ramos L. Role of Normal Stress in the Creep Dynamics and Failure of a Biopolymer Gel. PHYSICAL REVIEW LETTERS 2020; 125:268006. [PMID: 33449706 DOI: 10.1103/physrevlett.125.268006] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2020] [Revised: 11/06/2020] [Accepted: 12/08/2020] [Indexed: 06/12/2023]
Abstract
We investigate the delayed rupture of biopolymer gels under a constant shear load by simultaneous dynamic light scattering and rheology measurements. We unveil the crucial role of normal stresses built up during gelation: All samples that eventually fracture self-weaken during the gelation process, as revealed by a partial relaxation of the normal stress concomitant to a burst of microscopic plastic rearrangements. Upon applying a shear stress, weakened gels exhibit in the creep regime distinctive signatures in their microscopic dynamics, which anticipate macroscopic fracture by up to thousands of seconds. The dynamics in fracturing gels are faster than those of nonfracturing gels and exhibit large spatiotemporal fluctuations. A spatially localized region with significant plasticity eventually nucleates, expands progressively, and finally invades the whole sample, triggering macroscopic failure.
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Affiliation(s)
- Angelo Pommella
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - Luca Cipelletti
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
| | - Laurence Ramos
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France
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Divoux T, Shukla A, Marsit B, Kaloga Y, Bischofberger I. Criterion for Fingering Instabilities in Colloidal Gels. PHYSICAL REVIEW LETTERS 2020; 124:248006. [PMID: 32639838 DOI: 10.1103/physrevlett.124.248006] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Accepted: 05/15/2020] [Indexed: 06/11/2023]
Abstract
We sandwich a colloidal gel between two parallel plates and induce a radial flow by lifting the upper plate at a constant velocity. Two distinct scenarios result from such a tensile test: (i) stable flows during which the gel undergoes a tensile deformation without yielding, and (ii) unstable flows characterized by the radial growth of air fingers into the gel. We show that the unstable regime occurs beyond a critical energy input, independent of the gel's macroscopic yield stress. This implies a local fluidization of the gel at the tip of the growing fingers and results in the most unstable wavelength of the patterns exhibiting the characteristic scalings of the classical viscous fingering instability. Our work provides a quantitative criterion for the onset of fingering in colloidal gels based on a local shear-induced yielding in agreement with the delayed failure framework.
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Affiliation(s)
- Thibaut Divoux
- MultiScale Material Science for Energy and Environment, UMI 3466, CNRS-MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Asheesh Shukla
- MultiScale Material Science for Energy and Environment, UMI 3466, CNRS-MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Badis Marsit
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yacouba Kaloga
- MultiScale Material Science for Energy and Environment, UMI 3466, CNRS-MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA
| | - Irmgard Bischofberger
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Ferreiro-Córdova C, Del Gado E, Foffi G, Bouzid M. Multi-component colloidal gels: interplay between structure and mechanical properties. SOFT MATTER 2020; 16:4414-4421. [PMID: 32337525 DOI: 10.1039/c9sm02410g] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of components leads to softer solids that can accommodate progressively larger strains before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work provides new insight into mechanisms at play for controlling the material properties and opens a road to new design principles for soft composite solids.
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