Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Unterberger, Michael Johannes; Weisbecker, Hannah; Holzapfel, Gerhard

doi:10.1016/j.ijnonlinmec.2014.09.017

Cited by 4 publications

(3 citation statements)

References 36 publications

(86 reference statements)

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“…Owing to the existent barriers to link the phenomena between different length and time scales, reviews on cross-linked networks were performed. 153,157,158 Regarding the molecular level, the mathematical formulations 159 usually cannot be directly visualised by the current experimental techniques and, while Mikado models are capable to capture protein unfolding and cross-linker kinetics on the network requiring high computational costs, the continuum models loose microstructural information because they involve an homogenisation of the actin filaments properties.…”

Section: Passive Behaviourmentioning

confidence: 99%

Cellular modelling in functional tissue engineering: review oriented for pelvic floor dysfunctions

Ferreira

Parente

Mascarenhas

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part L:

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This paper aims to review the current strategies for pelvic floor dysfunctions (PFDs). PFDs, such as stress urinary incontinence, foecal incontinence and vaginal prolapse affect the quality of life in women, involve high healthcare costs, and pose poor long-term success rates. As the problem progresses the cells in the pelvic tissues are impaired. The rheological relations between PFD and the damage of the tissues is not yet well established, bringing out clinical repair interventions, instead of knowing the root problem. As a consequence, the verification of damage mechanisms in the pelvic structures should be observed at cellular scales to correlate with the macroscopic phenomenological pathologies, namely, the changes in the mechanical properties and on the geometric configuration of the pelvic structures. Cells sense mechanical stimuli and respond biochemically via mechanotransduction mechanisms. Therefore, investigations on the cell dynamics must be performed, considering the physical conditions inside the bioreactors, to shed insight into the active behaviour of the cells during the treatment. These investigations should establish the conditions that push a cell to or keep a cell in a desired state during a regenerative treatment. This paper reviews the use of human adult stem cells to regenerate the defective muscles, ligaments and connective tissues in the pelvic floor, focusing on the role of the computational models as an assistive technology for these emergent tissue engineering treatments. First, the pelvic floor anatomy and physiology is related with the kinematic and mechanical behaviour of those structures at the tissue and cell scales. After, the relevance of the regenerative treatments is discussed and the requirements for their application are summarised. Later, the developments on computational models are exposed and the main guidelines for regeneration of the pelvic cavity tissues are proposed.

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Section: Passive Behaviourmentioning

confidence: 99%

Cellular modelling in functional tissue engineering: review oriented for pelvic floor dysfunctions

Ferreira

Parente

Mascarenhas

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part L:

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“…Away from equilibrium, we have found that this simple one-dimensional model has an elaborate steady-state phase diagram with transitions between different flowing phases. By choosing to represent the (x, y)-plane perpendicular to the direction of the 1D lattice, we can compare the model's local angular velocity with the rotation flow profile of a fluid in a parallel-plate rheometer [17,18]. Of course, our model is not truly three-dimensional like the fluid in a rheometric experiment, but it has many of the same features, including microscopic internal interactions, a macroscopic steady-state flow profile and shear rate, energy exchange, conserved angular momentum and torque propagation.…”

Section: Introductionmentioning

confidence: 99%

The simplest microscopic model of a complex fluid: flow phenomena and constitutive relation

Evans,

Hall,

Simha

et al. 2016

Preprint

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It was shown in [PRL 114, 138301 (2015)] that a remarkably simple dynamical model exhibits many of the complex flow regimes and non-equilibrium phase transitions characteristic of complex fluids. By removing extraneous detail, this simplest microscopic model of non-Newtonian flow can reveal the universal physics relevant to all complex fluids. Here we present more detailed results and a full derivation of the model's compact mean-field constitutive relation, with great potential scope for insights into universality and tractable mathematics. By enforcing local conservation of angular momentum, the one-dimensional (1D) XY-model (originally used for equilibrium magnetic systems) can be driven into various flow regimes, including simple Newtonian behaviour, shear banding, solidliquid coexistence and slip-plane motion. The model demonstrates that the phenomenon of shear banding does not rely on details of tensorial stress fields, but can exist in 1D.

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“…Hamilton's equations are recovered in the conservative case T = µ = 0. Although the model is insensitive to absolute rotational velocities, we can drive it into a non-equilibrium steady state by rotating one of its boundaries relative to the other (as in a parallel-plate rheometer shearing a sample of fluid [20][21][22]). To impose periodic boundary conditions whilst also applying a relative torque across the system, rotors at opposite ends of the chain are designated as neighbours, but see each other through an angular offset that increases at a constant angular velocity.…”

mentioning

confidence: 99%

ClassicalXYModel with Conserved Angular Momentum is an Archetypal Non-Newtonian Fluid

et al. 2015

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We find that the classical one-dimensional (1D) XY model, with angular-momentum-conserving Langevin dynamics, mimics the non-Newtonian flow regimes characteristic of soft matter when subjected to counter-rotating boundaries. An elaborate steady-state phase diagram has continuous and first-order transitions between states of uniform flow, shear-banding, solid-fluid coexistence and slip-planes. Results of numerically studies and a concise mean-field constitutive relation, offer a paradigm for diverse non-equilibrium complex fluids.

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Mechanical modeling of rheometer experiments: Applications to rubber and actin networks

Cited by 4 publications

References 36 publications

Cellular modelling in functional tissue engineering: review oriented for pelvic floor dysfunctions

Cellular modelling in functional tissue engineering: review oriented for pelvic floor dysfunctions

The simplest microscopic model of a complex fluid: flow phenomena and constitutive relation

ClassicalXYModel with Conserved Angular Momentum is an Archetypal Non-Newtonian Fluid

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