An energetic approach to the analysis of anisotropic hyperelastic materials

Federico, Salvatore; Grillo, Alfio; Imatani, Shōji; Giaquinta, G.; Herzog, Walter

doi:10.1016/j.ijengsci.2007.09.005

Cited by 27 publications

(24 citation statements)

References 37 publications

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“…Furthermore, the variational techniques presented in [56], being adapted to dissipative phenomena, may be used in this context. Finally, it seems attractive for the application of higher continuum models such as those described in [57][58][59][60]; damage detection referring to the procedure proposed by [61,62] which considers traveling loads as signals or in identification problems such as those described in [63][64][65][66]; the extension to plasticity for evaluating collapse load, see for example [67][68][69][70][71][72], or to piezoelectric materials, see [73,74], in the framework of structural control. The closed-form solution for load cases LC1 (bending couple, W) and LC2 (vertical force, P) are given in [33].…”

Section: Discussionmentioning

confidence: 99%

Constitutive models for strongly curved beams in the frame of isogeometric analysis

Cazzani

Malagù

Turco

et al. 2015

Mathematics and Mechanics of Solids

140

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The current development of the isogeometric approach in various fields of mechanics is explained by the high-accuracy results which can be achieved at a reduced computational cost by codes based on non-uniform rational B-splines (NURBS). In the case of strongly curved beams the simple diagonal de Saint-Venant’s constitutive model can lead to significant errors as it has been reported in the classic literature. Other models such as Winkler’s have been proposed and seem more suitable for these kinds of structures. Unfortunately several numerical codes are based on a diagonal constitutive model which neglects the coupling effect of elongation and curvature even if a highly refined geometry description can be developed by means of NURBS. The results obtained by means of numerical codes based on isogeometrical analysis for curved beams are here reported and basic choices, computational costs and numerical accuracy of the above-mentioned constitutive models are discussed, from a qualitative and quantitative point of view. This comparison, in the authors’ opinion, is necessary to avoid an excessive gap between the computational efficiency of NURBS, which are capable of very accurate geometry description, and a simplistic representation of the constitutive relations that is efficient for straight beams but not so much for curved beams whose curvature is large. The results of some selected tests are presented and discussed to highlight differences between the two approaches, showing that the small increase of computational cost of Winkler’s model is well compensated by the accuracy gain

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Section: Discussionmentioning

confidence: 99%

Constitutive models for strongly curved beams in the frame of isogeometric analysis

Cazzani

Malagù

Turco

et al. 2015

Mathematics and Mechanics of Solids

140

View full text Add to dashboard Cite

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“…applications to complex materials: composite, plastic, poro/two phases-elastic, or non-linear elastic ones, like, for instance, those described in [67][68][69][70][71][72][73]. …”

Section: Discussionmentioning

confidence: 99%

Continuous transition between traveling mass and traveling oscillator using mixed variables

Cazzani

Wagner

Rüge

et al. 2016

International Journal of Non-Linear Mechanics

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“…The surface-to-surface contact between the cartilage and the indenter was modeled as the frictionless contact. The boundary condition of the impermeable boundary between rigid indenter and cartilage was set based on previous studies (Federico et al, 2008;Li et al, 1999). Given that the stiffness of both the indenter and the bone are several orders of magnitude higher than that of the cartilage, both of them were modeled as rigid bodies.…”

Section: Porohyperelastic Modelmentioning

confidence: 99%

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

Thibbotuwawa

Oloyede

Senadeera

et al. 2015

Journal of the Mechanical Behavior of Biomedical Materials

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Solid-interstitial fluid interaction, which depends on tissue permeability, is significant to the strain-rate-dependent mechanical behavior of humeral head (shoulder) cartilage. Due to anatomical and biomechanical similarities to that of the human shoulder, kangaroos present a suitable animal model. Therefore, indentation experiments were conducted on kangaroo shoulder cartilage tissues from low (10(-4)/s) to moderately high (10(-2)/s) strain-rates. A porohyperelastic model was developed based on the experimental characterization; and a permeability function that takes into account the effect of strain-rate on permeability (strain-rate-dependent permeability) was introduced into the model to investigate the effect of rate-dependent fluid flow on tissue response. The prediction of the model with the strain-rate-dependent permeability was compared with those of the models using constant permeability and strain-dependent permeability. Compared to the model with constant permeability, the models with strain-dependent and strain-rate-dependent permeability were able to better capture the experimental variation at all strain-rates (p < 0.05). Significant differences were not identified between models with strain-dependent and strain-rate-dependent permeability at strain-rate of 5 × 10(-3)/s (p = 0.179). However, at strain-rate of 10(-2)/s, the model with strain-rate-dependent permeability was significantly better at capturing the experimental results (p < 0.005). The findings thus revealed the significance of rate-dependent fluid flow on tissue behavior at large strain-rates, which provides insights into the mechanical deformation mechanisms of cartilage tissues.

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An energetic approach to the analysis of anisotropic hyperelastic materials

Cited by 27 publications

References 37 publications

Constitutive models for strongly curved beams in the frame of isogeometric analysis

Constitutive models for strongly curved beams in the frame of isogeometric analysis

Continuous transition between traveling mass and traveling oscillator using mixed variables

Investigation of the mechanical behavior of kangaroo humeral head cartilage tissue by a porohyperelastic model based on the strain-rate-dependent permeability

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