An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects

Nedjar, Boumediene

doi:10.1016/j.cma.2006.09.009

Cited by 83 publications

(41 citation statements)

References 31 publications

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“…The particular approach for anisotropic viscoelastic effects follows the tensor formalism of Nguyen et al [148] and Nedjar [149] who introduced viscosity tensors. An essential feature of the model is that the matrix and the fibre phase are treated separately, each featuring their own deformation gradient.…”

Section: (I) Quasi-linear Viscoelasticity and Its Derivativesmentioning

confidence: 99%

Mathematical and computational modelling of skin biophysics: a review

Limbert

2017

Proc. R. Soc. A.

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The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

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Section: (I) Quasi-linear Viscoelasticity and Its Derivativesmentioning

confidence: 99%

Mathematical and computational modelling of skin biophysics: a review

Limbert

2017

Proc. R. Soc. A.

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“…As proposed by Nedjar [40] in the case of viscoelasticity, based on a similar treatment of elasto-plasticity by Klinkel et al [39], we also perform a decomposition of the chain deformation gradient as An additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts is done as shown in a previous paper [25] For a later use, we define the right Cauchy-Green deformation tensors The left Cauchy-Green deformation tensor is given by b = FF t . As G is idempotent, this gives…”

Section: Introductionmentioning

confidence: 99%

Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers

2014

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Iron-filled magnetorheological polymers, when cured in the presence of a magnetic field, result in having a transversely isotropic structure with iron particles forming chains along the direction of applied magnetic induction. In this work, we model the magneto-viscoelastic deformation (and magnetization) process of such polymers. Components of the deformation gradient and the applied magnetic induction in the direction of anisotropy are considered to be additional arguments of the energy density function. The existence of internal damping mechanisms is considered by performing a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts. Energy density functions and evolution laws of the internal variables are proposed that agree with the laws of thermodynamics. In the end, we present solutions of some standard deformation cases to illustrate the theory. In particular, it is shown that the orientation of resultant magnetic field and principal stress directions change with time owing to viscoelastic evolution.

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“…Since the dissipative phenomena can either be exhibited by the fibers or by the matrix, it is essential to consider the viscous effects within a phenomenological modeling framework. Such viscous effects have been studied in polymer-based composites [6,7]. There exist many techniques on the subject, mostly based on the correspondence principle.…”

Section: Introductionmentioning

confidence: 99%

The symplectic system method in the stress analysis of 2D elasto-viscoelastic fiber reinforced composites

Zhang

Xü

2009

Arch Appl Mech

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With the aid of the variational method and Laplace transformation, the symplectic system method is employed into two-dimensional elastic-viscoelastic fiber reinforced composites. The fundamental eigenfunctions of the governing equations are generalized to the time domain. Therefore the problem can be discussed directly in the time domain, and the iterative application of Laplace transformation is not needed. Using this method, all the stress components of the inner fiber and outer matrix, and hence the stress transfer in the interface between the fiber and matrix, are expressed analytically. The results obtained by the approach are accurate, because all the boundary conditions prescribed on the surfaces and ends of the composites can be satisfied. Numerical example demonstrate that both the shear stress and the normal stress decrease with time due to the viscoelastic property of the matrix, and that stress concentration occurs near the end.

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An anisotropic viscoelastic fibre–matrix model at finite strains: Continuum formulation and computational aspects

Cited by 83 publications

References 31 publications

Mathematical and computational modelling of skin biophysics: a review

Mathematical and computational modelling of skin biophysics: a review

Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers

The symplectic system method in the stress analysis of 2D elasto-viscoelastic fiber reinforced composites

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