An anisotropic fibre-matrix material model at finite elastic-plastic strains

Klinkel, Sven; Sansour, Carlo; Wagner, Werner

doi:10.1007/s00466-004-0629-2

Cited by 41 publications

(24 citation statements)

References 22 publications

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“…The directional responses of the fibres induce then an anisotropic behaviour of the whole composite in the equilibrium and non-equilibrium thermodynamic regimes. The resulting framework is very similar to that of the anisotropic elastoplasticity at finite strains recently proposed by Klinkel, Sansour and Wagner [11]. In addition to its conceptual simplicity, the numerical effort is of the order of that devoted for an isotropic viscoelastic computation.…”

Section: Introductionsupporting

confidence: 65%

“…The basic definitions follow closely those given by Klinkel, Sansour and Wagner [11] in anisotropic elastoplasticity. Before going on, and in all what follows, let ϕ(., t) denotes the motion in a time interval [0, T ] of a continuum body with reference configuration Ω 0 .…”

Section: Basic Kinematic Assumptionsmentioning

confidence: 90%

“…By analogy with the recent work in anisotropic elastoplasticity, see [11], the crucial idea is that the tensor F e F M F defines an equivalent class of elastically relaxing parts of the fibre family's deformation gradient. Then, introducing the following definition for the class:…”

Section: Basic Kinematic Assumptionsmentioning

confidence: 99%

“…Recently, a considerable effort has been devoted into the extension of isotropic finite strain inelastic models to the anisotropic case from the theoretical and the numerical points of view. We refer for example to the anisotropic elastoplastic formulations proposed by Spencer (2001) [32], Reese (2003) [20], Sansour and Bocko (2003) [23], and more recently by Klinkel, Sansour and Wagner (2005) [11]. And for anisotropic viscoelasticity, we refer for example to the recent formulation by Holzapfel and Gasser (2001) in [8], see also [9].…”

Section: Introductionmentioning

confidence: 99%

“…Note that this multiplicative decomposition, originally proposed by Sidoroff (1974) [26], has been deeply investigated by several other authors in the isotropic case, see for example [5,[12][13][14]21] among other references. On the other hand, the present approach considers the continuum as a superposition of the matrix and further one-dimensional continua, each of them representing one family of fibres, as recently proposed by Klinkel, Sansour and Wagner (2005) [11] in the context of finite anisotropic elastoplasticity. The different continua are implicitly linked by the kinematical constraint that the deformation gradient together with its multiplicative split apply to all of them.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Nedjar¹

2007

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionsupporting

confidence: 65%

Section: Basic Kinematic Assumptionsmentioning

confidence: 90%

Section: Basic Kinematic Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Nedjar¹

2007

Computer Methods in Applied Mechanics and Engineering

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Studying the influence of hydrogel injections into the infarcted left ventricle using the element‐free Galerkin method

Legner

Skatulla

Mbewu

et al. 2013

Numer Methods Biomed Eng

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Myocardial infarction is an increasing health problem worldwide. Because of an under-supply of blood, the cardiomyocytes in the affected region permanently lose their ability to contract. This in turn gradually weakens the overall heart function. A new therapeutic approach based on the injection of a gel into the infarcted area aims to support the healing and to inhibit adverse remodelling that can lead to heart failure. A computational model is the basis for obtaining a better understanding of the heart mechanics, in particular, how myocardial infarction and gel injections affect its pumping performance. A strain invariant-based stored energy function is proposed to account for the passive mechanical behaviour of the model, which also makes provision for active contraction. To incorporate injections an additive homogenization approach is introduced. The numerical framework is developed using an in-house code based on the element-free Galerkin method. The main focus of this contribution is to investigate the influence of gel injections on the mechanics of the left ventricle during the diastolic filling and systolic isovolumetric (isochoric) contraction phases. It is found that gel injections are able to reduce the elevated fibre stresses caused by an infarct.

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Strongly orthotropic continuum mechanics and finite element treatment

Kellermann

Furukawa

Kelly

2008

Numerical Meth Engineering

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SUMMARYDespite successful application to orthotropic analysis, any Lagrangian strain tensor that is symmetric can be classified as an isotropic metric, while the infinitely orthotropic case can be accurately dealt with using one-dimensional elements, structural tensors or kinematic constraints. In this paper, we present a strongly orthotropic continuum mechanics basis that models the exact kinematic behavior of the intermediary class of materials and also show its application to multi-axial media and treatment using the finite element method. By asserting that mechanistic strain metrics must be material property dependent and satisfy equilibrium, we are able to derive a novel orthotropic linear strain tensor that is asymmetric and thus capable of describing all levels of orthotropy, while maintaining generality to the well-established isotropic approach. Subsequently formulated are a material principal rotation tensor, extended orthotropic compliance tensor and an extended Mohr's plot for strain relying on an additional metric denoted as aspectual strain. Using the developed finite element formulation, it is shown that identical stress results to conventional theory for an orthotropic linear problem are predicted, while offering a more informative analysis. A second numerical example demonstrates the unique capability of this approach to solve the erroneous response of strongly orthotropic materials under trellis shear as compared with a number of conventional and contemporary approaches and thus its ability to produce kinematically exact results.

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An anisotropic fibre-matrix material model at finite elastic-plastic strains

Cited by 41 publications

References 22 publications

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

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

Studying the influence of hydrogel injections into the infarcted left ventricle using the element‐free Galerkin method

Strongly orthotropic continuum mechanics and finite element treatment

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