Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials

Grillo, Alfio; Federico, Salvatore; Wittum, Gabriel

doi:10.1016/j.ijnonlinmec.2011.09.026

Cited by 73 publications

(75 citation statements)

References 57 publications

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“…This aspect of the mechanics of these fabrics will be the subject of future investigations. Also very relevant may be the implications of the results presented here on the understanding of the biomechanics of living tissues: Indeed (see e.g., [26,[31][32][33] and [36][37][38]), the role of fiber reinforcements on the mechanical behavior of growing and reconstructed tissues is attracting some attention. Finally, the consideration of multiphysics effects (as for instance piezo-or flexo-electricity) in systems having the geometry and the kinematics of a pantographic sheet can also disclose new possibilities (see [20,27]).…”

mentioning

confidence: 99%

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

Dell’Isola

Lekszycki

Pawlikowski

et al. 2015

Z. Angew. Math. Phys.

158

117

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mentioning

confidence: 99%

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

Dell’Isola

Lekszycki

Pawlikowski

et al. 2015

Z. Angew. Math. Phys.

158

117

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“…Transforming (5a) by the backward Piola transformation induced by the solid motion χ( · , t), and writing the transformed equation once for α = s and once for α = f, it is possible to show that, after some manipulations, the mass balance laws for the solid and the fluid phase reduce to [44,45] …”

Section: Dynamics Of Biphasic Mixturesmentioning

confidence: 99%

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Grillo

Prohl

Wittum

2015

Continuum Mech. Thermodyn.

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We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of "plastic" distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

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“…The material equations (54) have been shown for the case of Darcy's law [1,3,11,[15][16][17]23,25], as well as for the analogous case of the polarisation of a dielectric [5,6,9,19,26,27], in the traditional manner, without the use of differential forms. In some cases, the flux density pseudo-vector w may be given as the product of a pseudo-scalar density ρ times a proper vector field v, i.e.…”

Section: Application To First-order Transport Lawsmentioning

confidence: 99%

Material description of fluxes in terms of differential forms

Federico

Grillo

Segev

2015

Continuum Mech. Thermodyn.

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The flux of a certain extensive physical quantity across a surface is often represented by the integral over the surface of the component of a pseudo-vector normal to the surface. A pseudo-vector is in fact a possible representation of a second-order differential form, i.e. a skew-symmetric second-order covariant tensor, which follows the regular transformation laws of tensors. However, because of the skew-symmetry of differential forms, the associated pseudo-vector follows a transformation law that is different from that of proper vectors, and is named after the Italian mathematical physicist Gabrio Piola (1794-1850). In this work, we employ the methods of Differential Geometry and the representation in terms of differential forms to demonstrate how the flux of an extensive quantity transforms from the spatial to the material point of view. After an introduction to the theory of differential forms, their transformation laws, and their role in integration theory, we apply them to the case of first-order transport laws such as Darcy's law and Ohm's law.

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Growth, mass transfer, and remodeling in fiber-reinforced, multi-constituent materials

Cited by 73 publications

References 57 publications

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

A poroplastic model of structural reorganisation in porous media of biomechanical interest

Material description of fluxes in terms of differential forms

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