Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials

Altmeyer, Guillaume; Panicaud, Benoît; Rouhaud, Emmanuelle; Wang, Mingchuan; Roos, Arjen; Kerner, Richard

doi:10.1007/s00161-016-0507-0

Cited by 8 publications

(5 citation statements)

References 31 publications

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“…However, the real deformation processes are dissipative, as follows from the second law of thermodynamics. There is an extensive literature regarding different rheological effects which are observed in real materials (e.g., stress relaxation, hysteresis loop, Mullins effect, strain rate dependence, etc., cf [2,13,25,30,31]). The analyzed deviation of the conditions presented by Rivlin and Saunders from the mathematical conditions of energy polyconvexity can be interpreted as the influence of dissipative processes that were registered experimentally but not analyzed in [24].…”

Section: Discussionmentioning

confidence: 99%

“…In the case of elastomers, the hyperelasticity theory is usually used to describe the material behavior, cf, e.g., [12,22]. Nowadays the hyperelasticity is also a basis utilized to formulate some more elaborate constitutive equations, such as the nonlinear viscoelastic or the damage models, e.g., [2,13,25,30,31]. Furthermore, the hyperelastic material models can be used for solving multifield problems, e.g., [8].…”

Section: Introductionmentioning

confidence: 99%

“…The constitutive models of hyperelasticity are viewed here as tools developed in order to solve different boundary value problems both analytically or numerically using the FE analysis, for instance. Thus, assuming the elastic energy as a polyconvex function appears to be a natural choice, since it ensures the existence of solution to a properly defined boundary value problem 2 . Other mathematical conditions such as the stored energy's positivity or the condition of convexity with respect to the principal stretches are either insufficient or too restrictive, cf [3,14,27].…”

Section: Introductionmentioning

confidence: 99%

“…In this study the Nelder-Mead optimization algorithm offered by Scilab software[4] and the quasi-Newton method available in Mathematica software[29] were utilized for the material parameter identification 2. A solution may also exist when the stored energy function is nonpolyconvex.…”

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confidence: 99%

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Polyconvex hyperelastic modeling of rubberlike materials

Suchocki

Jemioło

2021

J Braz. Soc. Mech. Sci. Eng.

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In this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Polyconvex hyperelastic modeling of rubberlike materials

Suchocki

Jemioło

2021

J Braz. Soc. Mech. Sci. Eng.

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“…In his relativistic thermodynamics ( [23,24]), Souriau proposed to generalize the second principle as ∇ α S α ≥ 0 and introduced the friction tensor f αβ = 1 2 (∇ α b β + ∇ β b α ) that merges the temperature gradient and the strain rate tensor, allowing to extend Fourier's conduction law and viscous flow rules to Relativity, as proposed by Vallée [25,26]. By the way, Relativity is a consistent framework for the hypoelastic, hyperelastic and dissipative constitutive laws [27][28][29].…”

Section: Relativistic Dynamics and Thermodynamicsmentioning

confidence: 99%

Lie groups and continuum mechanics: where do we stand today?

de Saxcé,

Razafindralandy

2024

Comptes Rendus. Mécanique

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Internal resonance and bending analysis of thick visco-hyper-elastic arches

Khaniki

Ghayesh

Chin

et al. 2022

Continuum Mech. Thermodyn.

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In this study, a comprehensive analysis of visco-hyper-elastic thick soft arches under an external time-independent as well as time-dependent loads is presented from bending and internal resonance phenomenon perspectives. Axial, transverse and rotation motions are considered for modelling the thick and soft arch in the framework of the Mooney–Rivlin and Kelvin–Voigt visco-hyper-elastic schemes and third-order shear deformable models. The arch is assumed to be incompressible and is modelled using von Kármán geometric nonlinearity in the strain–displacement relationship. Using a virtual work method, the bending equations are derived. For the vibration analysis, three, coupled, highly nonlinear equations of motions are obtained using force-moment balance method. The Newton–Raphson method together with the dynamic equilibrium technique is used for the bending and vibration analyses. A detailed study on the influence of having visco-hyper-elasticity and arch curvature in the frequency response of the system is given in detail, and the bending deformation due to the applied static load is presented. The influence of having thick, soft arches with different slenderness ratios is shown, and the forced vibration response is discussed. Moreover, internal resonance in the system is studied showing that the curvature term in the structure can lead to three-to-one internal resonances, showing a rich nonlinear frequency response. The results of this study are a step forward in studying the visco-hyper-elastic behaviour of biological structures and soft tissues. Graphic abstract

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Viscoelasticity behavior for finite deformations, using a consistent hypoelastic model based on Rivlin materials

Cited by 8 publications

References 31 publications

Polyconvex hyperelastic modeling of rubberlike materials

Polyconvex hyperelastic modeling of rubberlike materials

Lie groups and continuum mechanics: where do we stand today?

Internal resonance and bending analysis of thick visco-hyper-elastic arches

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