Torque-induced reorientation in active fibre-reinforced materials

Ciambella, Jacopo; Nardinocchi, Paola

doi:10.1039/c8sm02346h

Cited by 13 publications

(14 citation statements)

References 41 publications

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“…More importantly, during the experimental tests there are remodelling effects related to the internal reorganization of the cytoskeleton and of the stress fibers. Introducing remodelling into the continuum structure of the model as done in Ciambella and Nardinocchi (2019), Ciambella and Nardinocchi (2020) could allow to explore this effect, maybe improving the description of such a complex behaviour of the cells.…”

Section: Discussionmentioning

confidence: 99%

A nonlinear elastic description of cell preferential orientations over a stretched substrate

Lucci

Preziosi

2021

Biomech Model Mechanobiol

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The active response of cells to mechanical cues due to their interaction with the environment has been of increasing interest, since it is involved in many physiological phenomena, pathologies, and in tissue engineering. In particular, several experiments have shown that, if a substrate with overlying cells is cyclically stretched, they will reorient to reach a well-defined angle between their major axis and the main stretching direction. Recent experimental findings, also supported by a linear elastic model, indicated that the minimization of an elastic energy might drive this reorientation process. Motivated by the fact that a similar behaviour is observed even for high strains, in this paper we address the problem in the framework of finite elasticity, in order to study the presence of nonlinear effects. We find that, for a very large class of constitutive orthotropic models and with very general assumptions, there is a single linear relationship between a parameter describing the biaxial deformation and $$\cos ^2\theta _{\mathrm{eq}}$$ cos 2 θ eq , where $$\theta _{\mathrm{eq}}$$ θ eq is the orientation angle of the cell, with the slope of the line depending on a specific combination of four parameters that characterize the nonlinear constitutive equation. We also study the effect of introducing a further dependence of the energy on the anisotropic invariants related to the square of the Cauchy–Green strain tensor. This leads to departures from the linear relationship mentioned above, that are again critically compared with experimental data.

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Section: Discussionmentioning

confidence: 99%

A nonlinear elastic description of cell preferential orientations over a stretched substrate

Lucci

Preziosi

2021

Biomech Model Mechanobiol

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“…In this paper we have introduced a theoretical framework to define a non- First, the proposed framework can be extended to incorporate the possibility for the fibre to reorient independently of the viscous deformation as proposed by the authors in [45,30]. The present model would then be recovered by imposing a suitable constraint on the fibre rotation.…”

Section: Discussionmentioning

confidence: 99%

A structurally frame-indifferent model for anisotropic visco-hyperelastic materials

Ciambella,

Nardinocchi

2020

Preprint

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One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed thoroughly and addressed by introducing a novel anisotropic remodelling equation compatible with the principle of structural frame indifference, a requirement that every inelastic theory based on the multiplicative decomposition of the deformation gradient must obey to. The evolution laws of the dissipative process are completely determined by two scalar functions, the elastic strain energy and the dissipation densities. The proper choice of the dissipation function allows us to reduce the proposed model to the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to the anisotropic hyperelastic solid for fast deformations. Finally, a few prototype examples are discussed to highlight the role of the relaxation times in the constitutive response.

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“…( 6.38) is the growth of anisotropic tissues where the reinforcing fibre structure does not evolve from the reference configuration to the natural state, and the external field sym Y is used to bring into the modelling the effects of external stimuli [5]. We finally note that by assuming F g = I, that is, F e = F, the present formulation does not allow us to recover the elastic reorientation theory presented in [18]. In fact, by assuming F g ≡ 0, we would have L g = 0, D g = W g = 0 and, hence Ω = 0.…”

Section: The Reduced Evolution Problemsmentioning

confidence: 93%

“…proved true for a transversely isotropic material in [18]. It is worth remarking that M = C e Ŝe is the so-called Mandel stress, for which skw {M} =…”

Section: Thermodynamic Consistency Of the Constitutive Equationsmentioning

confidence: 98%

“…Recently, we have studied fiber reorientation in elastic materials and considered both passive reorientation [18], driven by mechanical loads, and active reorientation [19], driven by magnetic fields. We also presented and discussed a structurally frame-indifferent model for anisotropic viscohyperelastic materials [12] based on the evolution laws of the dissipative processes, which are completely determined by two scalar functions, the elastic strain energy and the dissipation densities.…”

Section: Our Contributionmentioning

confidence: 99%

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Non-affine fiber reorientation in finite inelasticity

Ciambella¹,

Nardinocchi²

2022

Preprint

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This paper introduces a model for the mechanical response of anisotropic soft materials undergoing large inelastic deformations. The composite is constituted by a soft isotropic matrix reinforced with stiff fibres, that can evolve independently from each other. The constitutive equations are provided in terms of the free energy density and the dissipation density which are both required to be thermodynamically consistent and structurally frame-indifferent, i.e., they must be independent of a rotation overimposed on the natural state. This is in contrast to many of the currently used inelastic models for soft fiber-reinforced materials which do not deal with the lack of uniqueness of the natural state. A constraint between the inelastic spin of the matrix and the rotation spin of the fibre is introduced to fully determined the natural state. The resulting flow rules of the inelastic processes incorporate some typical scenarios including viscoelasticity and growth.

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Torque-induced reorientation in active fibre-reinforced materials

Cited by 13 publications

References 41 publications

A nonlinear elastic description of cell preferential orientations over a stretched substrate

A nonlinear elastic description of cell preferential orientations over a stretched substrate

A structurally frame-indifferent model for anisotropic visco-hyperelastic materials

Non-affine fiber reorientation in finite inelasticity

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