1
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Wei X, Junot G, Golestanian R, Zhou X, Wang Y, Tierno P, Meng F. Molecular dynamics simulations of microscopic structural transition and macroscopic mechanical properties of magnetic gels. J Chem Phys 2024; 161:074902. [PMID: 39145560 DOI: 10.1063/5.0210769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2024] [Accepted: 07/25/2024] [Indexed: 08/16/2024] Open
Abstract
Magnetic gels with embedded micro-/nano-sized magnetic particles in cross-linked polymer networks can be actuated by external magnetic fields, with changes in their internal microscopic structures and macroscopic mechanical properties. We investigate the responses of such magnetic gels to an external magnetic field, by means of coarse-grained molecular dynamics simulations. We find that the dynamics of magnetic particles are determined by the interplay of magnetic dipole-dipole interactions, polymer elasticity, and thermal fluctuations. The corresponding microscopic structures formed by the magnetic particles, such as elongated chains, can be controlled by the external magnetic field. Furthermore, the magnetic gels can exhibit reinforced macroscopic mechanical properties, where the elastic modulus increases algebraically with the magnetic moments of the particles in the form of ∝(m-mc)2 when magnetic chains are formed. This simulation work can not only serve as a tool for studying the microscopic and the macroscopic responses of the magnetic gels, but also facilitate future fabrications and practical controls of magnetic composites with desired physical properties.
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Affiliation(s)
- Xuefeng Wei
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
| | - Gaspard Junot
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
| | - Ramin Golestanian
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - Xin Zhou
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
| | - Yanting Wang
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
| | - Pietro Tierno
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems, 08028 Barcelona, Spain
- Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, 08028 Barcelona, Spain
| | - Fanlong Meng
- Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou, Zhejiang 325000, China
- CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing 100049, China
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2
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Chen S, Markovich T, MacKintosh FC. Effective medium theory for mechanical phase transitions of fiber networks. SOFT MATTER 2023; 19:8124-8135. [PMID: 37846933 DOI: 10.1039/d3sm00810j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2023]
Abstract
Networks of stiff fibers govern the elasticity of biological structures such as the extracellular matrix of collagen. These networks are known to stiffen nonlinearly under shear or extensional strain. Recently, it has been shown that such stiffening is governed by a strain-controlled athermal but critical phase transition, from a floppy phase below the critical strain to a rigid phase above the critical strain. While this phase transition has been extensively studied numerically and experimentally, a complete analytical theory for this transition remains elusive. Here, we present an effective medium theory (EMT) for this mechanical phase transition of fiber networks. We extend a previous EMT appropriate for linear elasticity to incorporate nonlinear effects via an anharmonic Hamiltonian. The mean-field predictions of this theory, including the critical exponents, scaling relations and non-affine fluctuations qualitatively agree with previous experimental and numerical results.
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Affiliation(s)
- Sihan Chen
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA.
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
| | - Tomer Markovich
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
- School of Mechanical Engineering, Tel Aviv University, Tel Aviv 69978, Israel
- Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 69978, Israel
| | - Fred C MacKintosh
- Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA.
- Center for Theoretical Biological Physics, Rice University, Houston, TX 77005, USA
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA
- Department of Chemistry, Rice University, Houston, TX 77005, USA
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3
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Ruiz-Franco J, Tauber J, van der Gucht J. Cross-linker Mobility Governs Fracture Behavior of Catch-Bonded Networks. PHYSICAL REVIEW LETTERS 2023; 130:118203. [PMID: 37001087 DOI: 10.1103/physrevlett.130.118203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 01/24/2023] [Indexed: 06/19/2023]
Abstract
While most chemical bonds weaken under the action of mechanical force (called slip bond behavior), nature has developed bonds that do the opposite: their lifetime increases as force is applied. While such catch bonds have been studied quite extensively at the single molecule level and in adhesive contacts, recent work has shown that they are also abundantly present as crosslinkers in the actin cytoskeleton. However, their role and the mechanism by which they operate in these networks have remained unclear. Here, we present computer simulations that show how polymer networks crosslinked with either slip or catch bonds respond to mechanical stress. Our results reveal that catch bonding may be required to protect dynamic networks against fracture, in particular for mobile linkers that can diffuse freely after unbinding. While mobile slip bonds lead to networks that are very weak at high stresses, mobile catch bonds accumulate in high stress regions and thereby stabilize cracks, leading to a more ductile fracture behavior. This allows cells to combine structural adaptivity at low stresses with mechanical stability at high stresses.
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Affiliation(s)
- José Ruiz-Franco
- Physical Chemistry and Soft Matter, Wageningen University and Research, Stippeneng 4, 6708WE Wageningen, Netherlands
| | - Justin Tauber
- Physical Chemistry and Soft Matter, Wageningen University and Research, Stippeneng 4, 6708WE Wageningen, Netherlands
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University and Research, Stippeneng 4, 6708WE Wageningen, Netherlands
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4
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Syed S, MacKintosh FC, Shivers JL. Structural Features and Nonlinear Rheology of Self-Assembled Networks of Cross-Linked Semiflexible Polymers. J Phys Chem B 2022; 126:10741-10749. [PMID: 36475770 DOI: 10.1021/acs.jpcb.2c05439] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Disordered networks of semiflexible filaments are common support structures in biology. Familiar examples include fibrous matrices in blood clots, bacterial biofilms, and essential components of cells and tissues of plants, animals, and fungi. Despite the ubiquity of these networks in biomaterials, we have only a limited understanding of the relationship between their structural features and their highly strain-sensitive mechanical properties. In this work, we perform simulations of three-dimensional networks produced by the irreversible formation of cross-links between linker-decorated semiflexible filaments. We characterize the structure of networks formed by a simple diffusion-dependent assembly process and measure their associated steady-state rheological features at finite temperature over a range of applied prestrains that encompass the strain-stiffening transition. We quantify the dependence of network connectivity on cross-linker availability and detail the associated connectivity dependence of both linear elasticity and nonlinear strain-stiffening behavior, drawing comparisons with prior experimental measurements of the cross-linker concentration-dependent elasticity of actin gels.
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Affiliation(s)
- Saamiya Syed
- College of Technology, University of Houston, Houston, Texas 77204, United States.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States
| | - Fred C MacKintosh
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States.,Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics & Astronomy, Rice University, Houston, Texas 77005, United States
| | - Jordan L Shivers
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, United States.,Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States
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5
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Arzash S, Sharma A, MacKintosh FC. Mechanics of fiber networks under a bulk strain. Phys Rev E 2022; 106:L062403. [PMID: 36671162 DOI: 10.1103/physreve.106.l062403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Biopolymer networks are common in biological systems from the cytoskeleton of individual cells to collagen in the extracellular matrix. The mechanics of these systems under applied strain can be explained in some cases by a phase transition from soft to rigid states. For collagen networks, it has been shown that this transition is critical in nature and it is predicted to exhibit diverging fluctuations near a critical strain that depends on the network's connectivity and structure. Whereas prior work focused mostly on shear deformation that is more accessible experimentally, here we study the mechanics of such networks under an applied bulk or isotropic extension. We confirm that the bulk modulus of subisostatic fiber networks exhibits similar critical behavior as a function of bulk strain. We find different nonmean-field exponents for bulk as opposed to shear. We also confirm a similar hyperscaling relation to what was previously found for shear.
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Affiliation(s)
- Sadjad Arzash
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Abhinav Sharma
- Leibniz-Institut für Polymerforschung Dresden, Institut Theorie der Polymere, 01069 Dresden, Germany
| | - Fred C MacKintosh
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics & Astronomy, Rice University, Houston, Texas 77005, USA
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6
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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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7
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Arzash S, Shivers JL, MacKintosh FC. Shear-induced phase transition and critical exponents in three-dimensional fiber networks. Phys Rev E 2021; 104:L022402. [PMID: 34525571 DOI: 10.1103/physreve.104.l022402] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 07/29/2021] [Indexed: 11/07/2022]
Abstract
When subject to applied strain, fiber networks exhibit nonlinear elastic stiffening. Recent theory and experiments have shown that this phenomenon is controlled by an underlying mechanical phase transition that is critical in nature. Growing simulation evidence points to non-mean-field behavior for this transition and a hyperscaling relation has been proposed to relate the corresponding critical exponents. Here, we report simulations on two distinct network structures in three dimensions. By performing a finite-size scaling analysis, we test hyperscaling and identify various critical exponents. From the apparent validity of hyperscaling, as well as the non-mean-field exponents we observe, our results suggest that the upper critical dimension for the strain-controlled phase transition is above three, in contrast to the jamming transition that represents another athermal, mechanical phase transition.
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Affiliation(s)
- Sadjad Arzash
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Jordan L Shivers
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Fred C MacKintosh
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA.,Departments of Chemistry and Physics & Astronomy, Rice University, Houston, Texas 77005, USA
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8
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Martikainen L, Bertula K, Turunen M, Ikkala O. Strain Stiffening and Negative Normal Force of Agarose Hydrogels. Macromolecules 2020; 53:9983-9992. [PMID: 33250522 PMCID: PMC7690039 DOI: 10.1021/acs.macromol.0c00601] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2020] [Revised: 08/24/2020] [Indexed: 11/28/2022]
Abstract
Inspired by the specific strain stiffening and negative normal force phenomena in several biological networks, herein, we show strain stiffening and negative normal force in agarose hydrogels. We use both pre-strain and strain amplitude sweep protocols in dynamic rheological measurements where the gel slip was suppressed by the in situ gelation in the cross-hatched parallel plate rheometer geometry. Within the stiffening region, we show the scaling relation for the differential modulus K ∝ σ1, where σ is stress. The strain at the onset of stiffening is almost constant throughout the concentration range. The gels show negative apparent normal stress difference when sheared as a result of the gel contraction. The pore size of the hydrogel is large enough to allow water to move with respect to the network to balance the pressure difference caused by the hoop stress. The rheological analysis together with scanning electron microscopy suggests that the agarose gels can be described using subisostatic athermal network models where the connectivity dictates the stiffening behavior. Therefore, the simple agarose gels appear to capture several of the viscoelastic properties, which were previously thought to be characteristic to biological protein macromolecules.
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Affiliation(s)
- Lahja Martikainen
- Department
of Applied Physics, Molecular Materials Group, Aalto University School of Science, FI-00076 Espoo, Finland
| | - Kia Bertula
- Department
of Applied Physics, Molecular Materials Group, Aalto University School of Science, FI-00076 Espoo, Finland
| | - Matti Turunen
- Department
of Applied Physics, Molecular Materials Group, Aalto University School of Science, FI-00076 Espoo, Finland
| | - Olli Ikkala
- Department
of Applied Physics, Molecular Materials Group, Aalto University School of Science, FI-00076 Espoo, Finland
- Department
of Bioproducts and Biosystems, Aalto University
School of Chemical Engineering, FI-00076 Espoo, Finland
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9
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Arzash S, Shivers JL, MacKintosh FC. Finite size effects in critical fiber networks. SOFT MATTER 2020; 16:6784-6793. [PMID: 32638813 DOI: 10.1039/d0sm00764a] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Fibrous networks such as collagen are common in physiological systems. One important function of these networks is to provide mechanical stability for cells and tissues. At physiological levels of connectivity, such networks would be mechanically unstable with only central-force interactions. While networks can be stabilized by bending interactions, it has also been shown that they exhibit a critical transition from floppy to rigid as a function of applied strain. Beyond a certain strain threshold, it is predicted that underconstrained networks with only central-force interactions exhibit a discontinuity in the shear modulus. We study the finite-size scaling behavior of this transition and identify both the mechanical discontinuity and critical exponents in the thermodynamic limit. We find both non-mean-field behavior and evidence for a hyperscaling relation for the critical exponents, for which the network stiffness is analogous to the heat capacity for thermal phase transitions. Further evidence for this is also found in the self-averaging properties of fiber networks.
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Affiliation(s)
- Sadjad Arzash
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, TX 77005, USA. and Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA
| | - Jordan L Shivers
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, TX 77005, USA. and Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA
| | - Fred C MacKintosh
- Department of Chemical & Biomolecular Engineering, Rice University, Houston, TX 77005, USA. and Center for Theoretical Biological Physics, Rice University, Houston, TX 77030, USA and Departments of Chemistry and Physics & Astronomy, Rice University, Houston, TX 77005, USA
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10
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Shivers JL, Arzash S, MacKintosh FC. Nonlinear Poisson Effect Governed by a Mechanical Critical Transition. PHYSICAL REVIEW LETTERS 2020; 124:038002. [PMID: 32031850 DOI: 10.1103/physrevlett.124.038002] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Indexed: 06/10/2023]
Abstract
Under extensional strain, fiber networks can exhibit an anomalously large and nonlinear Poisson effect accompanied by a dramatic transverse contraction and volume reduction for applied strains as small as a few percent. We demonstrate that this phenomenon is controlled by a collective mechanical phase transition that occurs at a critical uniaxial strain that depends on network connectivity. This transition is punctuated by an anomalous peak in the apparent Poisson's ratio and other critical signatures such as diverging nonaffine strain fluctuations.
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Affiliation(s)
- Jordan L Shivers
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - Sadjad Arzash
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
| | - F C MacKintosh
- Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77030, USA
- Departments of Chemistry and Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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11
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Dussi S, Tauber J, van der Gucht J. Athermal Fracture of Elastic Networks: How Rigidity Challenges the Unavoidable Size-Induced Brittleness. PHYSICAL REVIEW LETTERS 2020; 124:018002. [PMID: 31976728 DOI: 10.1103/physrevlett.124.018002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2019] [Indexed: 06/10/2023]
Abstract
By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. We observe the largest damage in networks with connectivity close to the isostatic point and when the rupture thresholds are small. However, irrespective of network and spring properties, a more brittle fracture is observed upon increasing system size. Differently from most of the fracture descriptors, the maximum stress drop, a proxy for brittleness, displays a universal nonmonotonic dependence on system size. Based on this uncommon trend it is possible to identify the characteristic system size L^{*} at which brittleness kicks in. The more the disorder in network connectivity or in spring thresholds, the larger L^{*}. Finally, we speculate how this size-induced brittleness is influenced by thermal fluctuations.
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Affiliation(s)
- Simone Dussi
- Physical Chemistry and Soft Matter, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, Netherlands
| | - Justin Tauber
- Physical Chemistry and Soft Matter, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, Netherlands
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, Netherlands
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12
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Mann A, Sopher RS, Goren S, Shelah O, Tchaicheeyan O, Lesman A. Force chains in cell-cell mechanical communication. J R Soc Interface 2019; 16:20190348. [PMID: 31662075 DOI: 10.1098/rsif.2019.0348] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Force chains (FCs) are a key determinant of the micromechanical properties and behaviour of heterogeneous materials, such as granular systems. However, less is known about FCs in fibrous materials, such as the networks composing the extracellular matrix (ECM) of biological systems. Using a finite-element computational model, we simulated the contraction of a single cell and two nearby cells embedded in two-dimensional fibrous elastic networks and analysed the tensile FCs that developed in the ECM. The role of ECM nonlinear elasticity on FC formation was evaluated by considering linear and nonlinear, i.e. exhibiting 'buckling' and/or 'strain-stiffening', stress-strain curves. The effect of the degree of cell contraction and network coordination value was assessed. We found that nonlinear elasticity of the ECM fibres influenced the structure of the FCs, facilitating the transition towards more distinct chains that were less branched and more radially oriented than the chains formed in linear elastic networks. When two neighbouring cells contract, a larger number of FCs bridged between the cells in nonlinear networks, and these chains had a larger effective rigidity than the chains that did not reach a neighbouring cell. These results suggest that FCs function as a route for mechanical communication between distant cells and highlight the contribution of ECM fibre nonlinear elasticity to the formation of FCs.
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Affiliation(s)
- Amots Mann
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Ran S Sopher
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Shahar Goren
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Ortal Shelah
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Oren Tchaicheeyan
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
| | - Ayelet Lesman
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel
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13
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Bertula K, Martikainen L, Munne P, Hietala S, Klefström J, Ikkala O, Nonappa. Strain-Stiffening of Agarose Gels. ACS Macro Lett 2019; 8:670-675. [PMID: 35619522 DOI: 10.1021/acsmacrolett.9b00258] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Strain-stiffening is one of the characteristic properties of biological hydrogels and extracellular matrices, where the stiffness increases upon increased deformation. Whereas strain-stiffening is ubiquitous in protein-based materials, it has been less observed for polysaccharide and synthetic polymer gels. Here we show that agarose, that is, a common linear polysaccharide, forms helical fibrillar bundles upon cooling from aqueous solution. The hydrogels with these semiflexible fibrils show pronounced strain-stiffening. However, to reveal strain-stiffening, suppressing wall slippage turned as untrivial. Upon exploring different sample preparation techniques and rheological architectures, the cross-hatched parallel plate geometries and in situ gelation in the rheometer successfully prevented the slippage and resolved the strain-stiffening behavior. Combining with microscopy, we conclude that strain-stiffening is due to the semiflexible nature of the agarose fibrils and their geometrical connectivity, which is below the central-force isostatic critical connectivity. The biocompatibility and the observed strain-stiffening suggest the potential of agarose hydrogels in biomedical applications.
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Affiliation(s)
- Kia Bertula
- Department of Applied Physics, Molecular Materials Group, Aalto University School of Science, P.O. Box 15100, FI-00076, Espoo, Finland
| | - Lahja Martikainen
- Department of Applied Physics, Molecular Materials Group, Aalto University School of Science, P.O. Box 15100, FI-00076, Espoo, Finland
| | - Pauliina Munne
- Research Programs Unit/Translational Cancer Medicine Program and HiLIFE, University of Helsinki, P.O. Box 63, FI-00014, Helsinki, Finland
| | - Sami Hietala
- Department of Chemistry, University of Helsinki, P.O. Box 55, FI-00014, HU, Helsinki, Finland
| | - Juha Klefström
- Research Programs Unit/Translational Cancer Medicine Program and HiLIFE, University of Helsinki, P.O. Box 63, FI-00014, Helsinki, Finland
| | - Olli Ikkala
- Department of Applied Physics, Molecular Materials Group, Aalto University School of Science, P.O. Box 15100, FI-00076, Espoo, Finland
- Department of Bioproducts and Biosystems, Aalto University School of Chemical Engineering, P.O.
Box 15100, FI-00076, Espoo, Finland
| | - Nonappa
- Department of Applied Physics, Molecular Materials Group, Aalto University School of Science, P.O. Box 15100, FI-00076, Espoo, Finland
- Department of Bioproducts and Biosystems, Aalto University School of Chemical Engineering, P.O.
Box 15100, FI-00076, Espoo, Finland
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14
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Merkel M, Baumgarten K, Tighe BP, Manning ML. A minimal-length approach unifies rigidity in underconstrained materials. Proc Natl Acad Sci U S A 2019; 116:6560-6568. [PMID: 30894489 PMCID: PMC6452732 DOI: 10.1073/pnas.1815436116] [Citation(s) in RCA: 45] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
We present an approach to understand geometric-incompatibility-induced rigidity in underconstrained materials, including subisostatic 2D spring networks and 2D and 3D vertex models for dense biological tissues. We show that in all these models a geometric criterion, represented by a minimal length [Formula: see text], determines the onset of prestresses and rigidity. This allows us to predict not only the correct scalings for the elastic material properties, but also the precise magnitudes for bulk modulus and shear modulus discontinuities at the rigidity transition as well as the magnitude of the Poynting effect. We also predict from first principles that the ratio of the excess shear modulus to the shear stress should be inversely proportional to the critical strain with a prefactor of 3. We propose that this factor of 3 is a general hallmark of geometrically induced rigidity in underconstrained materials and could be used to distinguish this effect from nonlinear mechanics of single components in experiments. Finally, our results may lay important foundations for ways to estimate [Formula: see text] from measurements of local geometric structure and thus help develop methods to characterize large-scale mechanical properties from imaging data.
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Affiliation(s)
- Matthias Merkel
- Department of Physics, Syracuse University, Syracuse, NY 13244;
- Centre de Physique Théorique (CPT), Turing Center for Living Systems, Aix Marseille Univ, Université de Toulon, CNRS, 13009 Marseille, France
| | - Karsten Baumgarten
- Process & Energy Laboratory, Delft University of Technology, 2628 CB Delft, The Netherlands
| | - Brian P Tighe
- Process & Energy Laboratory, Delft University of Technology, 2628 CB Delft, The Netherlands
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, NY 13244
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