A nonlinear spectral rate-dependent constitutive equation for electro-viscoelastic solids

Shariff, M. H. B. M.; Bustamante, R.; Merodio, J.

doi:10.1007/s00033-020-01353-1

Cited by 13 publications

(5 citation statements)

References 39 publications

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“…The proposed potential function contains single variable functions that depend on a spectral invariant with a clear physical meaning; this facilitates the creation of specific forms of the total energy function, in the sense that a single variable function with a clear physical argument can be easily handled and is experimentally attractive. The advantages of spectral invariants over classical invariants [67] are discussed in reference [65]. After omitting the invariants e L and b L , we have shown that only 13 spectral invariants are independent, which is far less than the 37 classical invariants in the corresponding minimal integrity basis [67]; hence this may aid in reducing the complexity of modelling nonlinear residually stressed magneto-electro-elastic solids.…”

Section: Discussionmentioning

confidence: 95%

“…Advantages of spectral invariants over classical invariants are discussed, for example, in reference [65].…”

Section: Spectral Constitutive Equation: Time Independent Processesmentioning

confidence: 99%

“…We emphasize that the works of [14,15,25,26,44,47,51] uses non-spectral invariants, where most of them do not have clear physical meaning such as the classical invariants (or their variants) given in Spencer [67]; however, in this paper, our proposed formulation uses a set of spectral invariants [53,55,56,59,60,62,64], where each invariant has a clear physical meaning, and hence have an experimental advantage over other types of invariants with no physical interpretation such as the classical invariants [67]. The advantages of spectral invariants over classical invariants are discussed in [65]; hence, we will not elaborate them here. Following our recent work [11] on electro-magnetic-elastic materials, we briefly present the relevant and key governing equations that are essential to represent a magneto-electro-mechanically coupled system at large strains.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling the residually stressed magneto-electrically coupled soft elastic materials

Shariff

Hossain

Bustamante

et al. 2021

International Journal of Non-Linear Mechanics

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Section: Discussionmentioning

confidence: 95%

“…Advantages of spectral invariants over classical invariants are discussed, for example, in reference [65].…”

Section: Spectral Constitutive Equation: Time Independent Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling the residually stressed magneto-electrically coupled soft elastic materials

Shariff

Hossain

Bustamante

et al. 2021

International Journal of Non-Linear Mechanics

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“…In order to prevent any short-circuiting, a few millimeters (5-10 mm) area is kept uncoated on both sides throughout the entire length of the sample. Such experimental data help validating novel electro-mechanically coupled constitutive models at large strains [158] .…”

Section: Uniaxial Tensile Tests Experimental Characterizations Ofmentioning

confidence: 95%

Magneto‐/ electro‐responsive polymers toward manufacturing, characterization, and biomedical/ soft robotic applications

Yarali

Baniasadi

Zolfagharian

et al. 2022

Applied Materials Today

103

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“…There are various works regarding mechanical problems that corresponding to different aspects of constitutive models in recent decades (see [79], [124], [134], [135], [138], [157], [158], [169], [180],…”

Section: Mathematical Description Of the Problemmentioning

confidence: 99%

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Asghari

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This thesis deals with applying the sensitivity analysis methods that consideration of different functions on the non-linear elastic constitutive models in particular a circular cylindrical tube with radial and circumferential residual stresses and in some different types of pressure-inflation relation in a pressurized and axially stretched tube.Considering the inflation of hyperelastic cylinders in the framework of non-linear elastic constitutive models imposed to an axial stretch and torsion in the presence of residual stress has been done in this work. The constitutive relation of the material depends on various parameters such as the cylinder geometry, the different loading parameters, the prescribed stretches, and the magnitude of the residual stresses. Applying sensitivity analysis methods with attention to a statistical approach determined how the variations of the input variables affect the output variables.After reviewing on applied sensitivity analysis and recapping on basic contents of the non-linear elastic constitutive models, through the implementation of Sobol and the Fourier Amplitude Sensitivity Test (FAST) methods, the most important parameters of the system under the applied pressure and axial force such as the thickness of the tube or axial and azimuthal stretch are gained in the first part of the thesis. Then, the complicated form of the mechanical problem is expressed which is the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress which the input parameters in the material model are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In other words, the relation between various parameters as they relate to the inflation pressure, the moment, and the reduced axial force is studied with the help of two sensitivity analysis methods, namely, the Sobol method and FAST method. Both methods found their application in relatively complex models, especially when these models show a non-linear and non-monotonic behaviour. After that, the pressure-inflation relation in a pressurized and axially stretched tube is studied in fiber-reinforcement materials with different natural configurations. The material consists of an isotropic ground substance that is reinforced by two families of fibers. The natural configuration of the fibers may differ from that of the ground substance and the fibers are taken to be dispersed. The sensitivity analysis is applied by means of statistical simulation in the "R" program to determine how the uncertainties of the cylinder stretch, the fiber dispersion, and the fiber natural configuration affect the required inflation pressure. The V implementation of the Sobol and FAST methods allows us to account for the interplay of different parameters and to identify the most influential parameters in the pressure-inflation relation.

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A nonlinear spectral rate-dependent constitutive equation for electro-viscoelastic solids

Cited by 13 publications

References 39 publications

Modelling the residually stressed magneto-electrically coupled soft elastic materials

Modelling the residually stressed magneto-electrically coupled soft elastic materials

Magneto‐/ electro‐responsive polymers toward manufacturing, characterization, and biomedical/ soft robotic applications

Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

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