Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration

Hollenstein, Marc; Jabareen, Mahmood; Rubin, M. B.

doi:10.1007/s00466-013-0838-7

Cited by 59 publications

(42 citation statements)

References 22 publications

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“…the theoretical and numerical approach of Hollenstein et al [151] which can capture both rateindependent and rate-dependent anelastic response including stress relaxation effects. The model was applied to stress relaxation data of rabbit skin [54] with various degrees of success depending on the magnitude of stretch [150].…”

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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“…Procedures to integrate the evolution equations appearing in RB type models have been developed in [Rubin, 1989[Rubin, , 1996Rubin and Bodner, 2002], and recently by Rubin and Papes [2011] and Hollenstein et al [2013]. The numerical integration of the evolution equations (7) and (11) for m e and b e follows the predictor-corrector scheme used to compute the deviatoric elastic left Cauchy-Green tensor in [Rubin and Bodner, 2002, Appendix A].…”

Section: Numerical Frameworkmentioning

confidence: 99%

“…The numerical integration of the evolution equations (7) and (11) for m e and b e follows the predictor-corrector scheme used to compute the deviatoric elastic left Cauchy-Green tensor in [Rubin and Bodner, 2002, Appendix A]. The recent modifications to obtain the exact result in the case of zero dissipation [Rubin and Papes, 2011;Hollenstein et al, 2013;Flynn and Rubin, 2014], which adopt the idea of a relative deformation gradient from the configurations at time t n to t n+1 [see Simo, 1992;Simo and Hughes, 2000], have been included.…”

Section: Numerical Frameworkmentioning

confidence: 99%

“…With this, the estimator for b e at n+1 reads [cf. Rubin and Papes, 2011;Hollenstein et al, 2013;Flynn and Rubin, 2014] …”

Section: Numerical Frameworkmentioning

confidence: 99%

“…Rubin and Papes, 2011 ;Hollenstein et al, 2013]. For the present calculations, which were free of superimposed rigid body motions by definition, an efficient trapezoidal rule was applied, so that the update y = y n+1 in Eqns.…”

Section: Remarkmentioning

confidence: 99%

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A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

Mauri

Ehret

Focatiis

et al. 2015

Biomech Model Mechanobiol

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A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short-and long-term timedependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition * AM and AEE share first authorship of this article.

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A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model

Marinelli

Buscarnera

2018

Num Anal Meth Geomechanics

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Summary This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate‐dependent model defined within a breakage mechanics framework. For this purpose, a Generalized Backward Euler (GBE) algorithm has been implemented according to two different linearization strategies: The former is derived by a direct linearization of the constitutive equations, while the latter introduces rate effects through a consistency parameter. The accuracy and efficiency of the GBE algorithm have been investigated by (1) performing material point analyses and (2) solving initial boundary value problems. In both cases, the overall performance of the underlying algorithm is inspected for a range of loading rates, thus simulating comminution from slow to fast dynamic problems. As the viscous response of the breakage model can be recast through a viscous nucleus function, the presented algorithm can be considered as a general framework to integrate constitutive equations relying on the overstress approach typical of Perzyna‐like viscoplastic models.

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Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration

Cited by 59 publications

References 22 publications

Mathematical and computational modelling of skin biophysics: a review

Mathematical and computational modelling of skin biophysics: a review

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model

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