A framework for deformation, generalized diffusion, mass transfer and growth in multi-species multi-phase biological tissues

Loret, Benjamin; Simões, Fernando M. F.

doi:10.1016/j.euromechsol.2005.05.005

Cited by 67 publications

(63 citation statements)

References 37 publications

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“…Surface growth occurs when material is added to or removed from the surface of the body. To date, the literature of growth mechanics is overwhelmingly concerned with volumetric growth (Rodriguez et al 1994;Epstein & Maugin 2000;Lubarda & Hoger 2002;Garikipati et al 2004;Loret & Simoes 2005).…”

Section: Introductionmentioning

confidence: 99%

A continuum theory of surface growth

Hodge

Papadopoulos

2010

Proc. R. Soc. A.

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A continuum theory of surface growth in deformable bodies is presented. The theory employs a decomposition of the deformation and growth processes, which leads to a wellposed set of governing equations. It is argued that an evolving reference configuration is required to track the material points in the body. The balance laws are formulated with respect to a non-inertial frame of reference, which is used to track the motion of the body. A one-dimensional example problem is included to showcase the predictive capacity of the theory.

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Section: Introductionmentioning

confidence: 99%

A continuum theory of surface growth

Hodge

Papadopoulos

2010

Proc. R. Soc. A.

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“…We remark that in the presence of growth, or in the case of non-isochoric plastic distortions, the condition J p = 1 does not necessarily apply, which means that φ sR is not time-independent in general. Rather, in the presence of density-preserving growth [62,63], it can only be inferred that the volumetric fraction associated with the intermediate configuration, i.e. φ sn (X ) := J e (X, t)φ s (χ (X, t), t), is constant in time.…”

Section: Dynamics Of Biphasic Mixturesmentioning

confidence: 99%

“…In the first case, new material is either removed or laid over the pre-existing one [12]. In the second case, instead, the variation of mass can be diverted either in a change of volume or in a change of density of the system [31,62,63].…”

Section: Introductionmentioning

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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“…Another way to enrich the form of the elastic part at the left-hand side of the free energy in (39) is to adopt the multiplicative decomposition of the deformation tensor due to Rodriguez and co-authors [17]. This approach has been already proved to be effective in predicting the growth dynamics and residual stress emergence, in a mixture framework too [8,15] and is discussed in the next section.…”

Section: The Emergence Of Residual Stressmentioning

confidence: 99%

The insight of mixtures theory for growth and remodeling

Ambrosi

Preziosi

Vitale

2009

Z. Angew. Math. Phys.

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The emergence of residual stress as due to growth and remodeling of soft biological tissues is considered in the framework of the mixture theory. The focus is on mixtures composed by one elastic solid component and several fluid ones. It is shown that the standard theory is unable to predict residual stresses unless enriched by a suitable descriptor of growth. Both the introduction of a dependence of the free energy on the density of the solid component and the Kroner-Lee multiplicative decomposition of the gradient of deformation are effective in this respect, with different levels of generality. When adopting a multiplicative decomposition of the tensor gradient of deformation, thermodynamical arguments suggest constitutive laws for the evolution of the growth tensor that point out the role of the concentration of fluid species in driving the emergence of residual stress thanks to inhomogeneous growth.

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A framework for deformation, generalized diffusion, mass transfer and growth in multi-species multi-phase biological tissues

Cited by 67 publications

References 37 publications

A continuum theory of surface growth

A continuum theory of surface growth

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

The insight of mixtures theory for growth and remodeling

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