On a continuum thermodynamics formulation and computational aspects of finite growth in soft tissues

Nedjar, Boumediene

doi:10.1002/cnm.1448

Cited by 8 publications

(12 citation statements)

References 27 publications

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“…It is almost superfluous to remind ourselves that cellular mutations and interactions are essential in that case. Humphrey (2003) has reviewed results in biomechanics and has indicated trends on the matter (see also Athesian & Humphrey, 2012;Nedjar, 2011). Nontrivial theoretical issues are involved already at the level of the geometric description of the relevant processes.…”

Section: Micro-to-macro Interactionsmentioning

confidence: 98%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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Section: Micro-to-macro Interactionsmentioning

confidence: 98%

Mechanics of Material Mutations

Mariano

2014

Advances in Applied Mechanics

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“…Ogden (1997), Simo (1998), Holzapfel (2000, Nedjar (2002a,b, 2011), Wriggers (2008. Details of this nowadays standard notion are skipped here.…”

Section: Discussionmentioning

confidence: 99%

“…The useful kinematic relationship C F dF 2 Ṫ = is to be employed during the derivation, see Nedjar (2002Nedjar ( , 2007Nedjar ( , 2011 for similar developments. The following expression is then obtained …”

Section: Discussionmentioning

confidence: 99%

A theory of finite strain magneto-poromechanics

Nedjar

2015

Journal of the Mechanics and Physics of Solids

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International audienceThe main purpose of this paper is the multi-physics modeling of magnetically sensitive porous materials. We develop for this a magneto-poromechanics formulation suitable for the description of such a coupling. More specifically, we show how the current state of the art in the mathematical modeling of magneto-mechanics can easily be integrated within the unified framework of continuum thermodynamics of open media, which is crucial in setting the convenient forms of the state laws to fully characterize the behavior of porous materials. Moreover, due to the soft nature of these materials in general, the formulation is directly developed within the finite strain range. In a next step, a modeling example is proposed and detailed for the particular case of magneto-active foams with reversible deformations. In particular, due to their potentially high change in porosity, a nonlinear porosity law recently proposed is used to correctly describe the fluid flow through the interconnected pores when the solid skeleton is finitely strained causing fluid release or reabsorption. From the numerical point of view, the variational formulation together with an algorithmic design is described for an easy implementation within the context of the finite element method. Finally, a set of numerical simulations is presented to illustrate the effectiveness of the proposed framework

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“…During the computation, we need to calculate the principal Kirchhoff stresses so as to reconstitute the Kirchhoff stress tensor, see eq. (27). They are also needed for the computation of the tangent moduli.…”

Section: Application To the Exponentiated Hencky Strain Energymentioning

confidence: 99%

A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes

et al. 2017

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We investigate a finite element formulation of the exponentiated Hencky-logarithmic model whose strain energy function is given bywhere µ > 0 is the (infinitesimal) shear modulus, κ > 0 is the (infinitesimal) bulk modulus, k andk are additional dimensionless material parameters, U = √ F T F and V = √ F F T are the right and left stretch tensor corresponding to the deformation gradient F , log denotes the principal matrix logarithm on the set of positive definite symmetric matrices, devnX = X − trX n 1 and X = √ trX T X are the deviatoric part and the Frobenius matrix norm of an n × n-matrix X, respectively, and tr denotes the trace operator.To do so, the equivalent different forms of the constitutive equation are recast in terms of the principal logarithmic stretches by use of the spectral decomposition together with the undergoing properties. We show the capability of our approach with a number of relevant examples, including the challenging "eversion of elastic tubes" problem.

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On a continuum thermodynamics formulation and computational aspects of finite growth in soft tissues

Cited by 8 publications

References 27 publications

Mechanics of Material Mutations

Mechanics of Material Mutations

A theory of finite strain magneto-poromechanics

A finite element implementation of the isotropic exponentiated Hencky-logarithmic model and simulation of the eversion of elastic tubes

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