Computational modeling of the large deformation and flow of viscoelastic polymers

Shen, Tong; Long, Rong; Vernerey, Franck J.

doi:10.1007/s00466-018-1619-0

Cited by 17 publications

(11 citation statements)

References 77 publications

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“…Furthermore, the framework of this model is powerful because it is based on simple rules to describe the dynamics of tether behavior, and when applied to a population of tethers, it can predict the growth phenotype of different cells. The statistical model introduced in this work serves as a foundation for more extensive two-dimensional and three-dimensional models using concepts from the transient network theory that incorporates this approach in a more general framework (51,70,71). This would offer ripe ground for the investigation and discovery of new mechanisms in cell morphogenesis during growth, such as helical growth in P. blakesleeanus (39,40) and apical tip growth seen in pollen tubes, root hairs, and algal rhizoids (2,(72)(73)(74).…”

Section: Resultsmentioning

confidence: 99%

A Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces

Sridhar

Ortega

Vernerey

2018

Biophysical Journal

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Expansive growth is a process by which walled cells of plants, algae, and fungi use turgor pressure to mediate irreversible wall deformation and regulate their shape and volume. The molecular structure of the primary cell wall must therefore perform multiple functions simultaneously, including providing structural support by combining elastic and irreversible deformation and facilitating the deposition of new material during growth. This is accomplished by a network of microfibrils and tethers composed of complex polysaccharides and proteins that can dynamically mediate the network topology via periodic detachment and reattachment events. Lockhart and Ortega have provided crucial macroscopic understanding of the expansive growth process through global biophysical models, but these models lack the connection to molecular processes that trigger network rearrangements in the wall. Interestingly, the helical growth of the fungal sporangiophores of Phycomyces blakesleeanus is attributed to a limited region (called the growth zone) where microfibrils are deposited, followed by reorientation and slip. Based on past evidence of dominant shear strain between microfibrils (slippage), we propose a mechanistic model of a network of sliding fibrils connected by tethers. A statistical approach is introduced to describe the population behavior of tethers that have elastic properties and the ability to break and reform in time. These properties are responsible for global cell wall mechanics such as creep and stress relaxation. Model predictions are compared with experiments from literature on stress relaxation and turgor pressure step up for the growing cells of P. blakesleeanus, which are later extended to incised pea (Pisum sativus L.) and the algae Chara corallina using the unique dimensionless number P pe for each species. To our knowledge, this research is the first attempt to use a statistical approach to model the cell wall during expansive growth, and we believe it provides critical insights on cell wall dynamics at a molecular level.

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Section: Resultsmentioning

confidence: 99%

A Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces

Sridhar

Ortega

Vernerey

2018

Biophysical Journal

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“…The velocities at the next time increment were then determined by ensuring the equilibrium of material points via the standard equation r Á s ¼ 0. For additional details on the numerical approach, readers are referred to [32,33]. Figure 4 shows the deformation of the aggregation and stretch of active connections as a function of time for the quick load and release performed experimentally.…”

Section: Elastic Response and Stress Relaxationmentioning

confidence: 99%

How do fire ants control the rheology of their aggregations? A statistical mechanics approach

Vernerey¹,

Shen²,

Sridhar³

et al. 2018

J. R. Soc. Interface.

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Active networks are omnipresent in nature, from the molecular to the macro-scale. In this study, we explore the mechanical behaviour of fire ant aggregations, closely knit swarms that display impressive dynamics culminating with the aggregations’ capacity to self-heal and adapt to the environment. Although the combined elasticity and rheology of the ant aggregation can be characterized by phenomenological mechanical models (e.g. linear Maxwell or Kelvin–Voigt model), it is not clear how the behaviour of individual ants affects the aggregations’ emerging responses. Here, we explore an alternative way to think about these materials, describing them as a collection of individuals connected via elastic chains that associate and dissociate over time. Using our knowledge of these connections—e.g. their elasticity and attachment/dissociation rates—we construct a statistical description of connection stretch and derive an evolution equation for the corresponding stretch distribution. This time-evolving stretch distribution is then used to determine important macroscopic measures, e.g. stress, energy storage and energy dissipation, in the network. In this context, we show how the physical characteristics and activities of individual ants can explain the elasticity, flow and shear thinning of the aggregation. In particular, we find that experimental results are matched if the detachment rate between two individuals increases with tension in the connection.

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“…Finite Element Simulation of Fracture Experiment. The finite element simulation of fracture used a customized program written in Matlab developed in our previous studies (32,53). This program uses the coupled Eulerian-Lagrange description of kinematics and the TNT for material constitutive model.…”

Section: Methodsmentioning

confidence: 99%

Nonsteady fracture of transient networks: The case of vitrimer

Shen

Song

Cai

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number W0 that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can “program” a specimen’s crack extension dynamics by tuning the loading history.

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Computational modeling of the large deformation and flow of viscoelastic polymers

Cited by 17 publications

References 77 publications

A Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces

A Statistical Model of Expansive Growth in Plant and Fungal Cells: The Case of Phycomyces

How do fire ants control the rheology of their aggregations? A statistical mechanics approach

Nonsteady fracture of transient networks: The case of vitrimer

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