Advantages of formulating evolution equations for elastic-viscoplastic materials in terms of the velocity gradient instead of the spin tensor

Rubin, M. B.; Papes, O.

doi:10.2140/jomms.2011.6.529

Cited by 40 publications

(24 citation statements)

References 16 publications

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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%

See 2 more Smart Citations

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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Section: Numerical Frameworkmentioning

confidence: 99%

Section: Numerical Frameworkmentioning

confidence: 99%

See 1 more Smart Citation

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

View full text Add to dashboard Cite

show abstract

“…(7), (8) Following the work in [45][46][47], it is convenient to define the relative deformation gradient F r , the relative dilatation J r and the unimodular part F r of F r by the evolution equationṡ…”

Section: Robust Strongly Objective Numerical Integration Algorithmmentioning

confidence: 99%

Time-dependent behavior of passive skeletal muscle

Ahamed

Rubin

Trimmer

et al. 2015

Continuum Mech. Thermodyn.

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An isotropic three-dimensional nonlinear viscoelastic model is developed to simulate the timedependent behavior of passive skeletal muscle. The development of the model is stimulated by experimental data that characterize the response during simple uniaxial stress cyclic loading and unloading. Of particular interest is the rate-dependent response, the recovery of muscle properties from the preconditioned to the unconditioned state and stress relaxation at constant stretch during loading and unloading. The model considers the material to be a composite of a nonlinear hyperelastic component in parallel with a nonlinear dissipative component. The strain energy and the corresponding stress measures are separated additively into hyperelastic and dissipative parts. In contrast to standard nonlinear inelastic models, here the dissipative component is modeled using an evolution equation that combines rate-independent and rate-dependent responses smoothly with no finite elastic range. Large deformation evolution equations for the distortional deformations in the elastic and in the dissipative component are presented. A robust, strongly objective numerical integration algorithm is used to model rate-dependent and rate-independent inelastic responses. The constitutive formulation is specialized to simulate the experimental data. The nonlinear viscoelastic model accurately represents the time-dependent passive response of skeletal muscle.

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“…Thus, F r is independent of the choice of a reference configuration and can be obtained directly in terms of displacements of nodes in standard finite element procedures. At present, it is not known how to propose a strongly objective numerical integration procedure [9] for s i so the evolution equation (3.9) must be integrated by standard numerical approximations.…”

Section: Numerical Algorithm For Integration Of the Evolution Equatiomentioning

confidence: 99%

An Eulerian formulation for large deformations of anisotropic elastic and viscoelastic solids and viscous fluids

Rubin

Nadler

2015

Continuum Mech. Thermodyn.

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An Eulerian formulation has been developed for the constitutive response of a group of materials that includes anisotropic elastic and viscoelastic solids and viscous fluids. The material is considered to be a composite of an elastic solid and a viscous fluid. Evolution equations are proposed for a triad of vectors m i that represent the stretches and orientations of material line elements in the solid component. Evolution equations for an orthonormal triad of vectors s i are also proposed to characterize anisotropy of the fluid component. In particular, for an elastic solid it is shown that the material response is totally characterized by the functional form of the strain energy and by the current values of m i , which are measurable in the current state of the material. Moreover, it is shown that the proposed Eulerian formulation removes unphysical arbitrariness of the choice of the reference configuration in the standard formulation of constitutive equations for anisotropic elastic solids.

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Advantages of formulating evolution equations for elastic-viscoplastic materials in terms of the velocity gradient instead of the spin tensor

Cited by 40 publications

References 16 publications

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

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

Time-dependent behavior of passive skeletal muscle

An Eulerian formulation for large deformations of anisotropic elastic and viscoelastic solids and viscous fluids

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