Nonlinear axisymmetric vibrations of a hyperelastic orthotropic cylinder

Aranda-Iglesias, D.; Rodríguez-Martínez, J.A.; Rubin, M. B.

doi:10.1016/j.ijnonlinmec.2017.11.007

Cited by 17 publications

(5 citation statements)

References 39 publications

(86 reference statements)

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“…In ( 9)- (10), the strict inequality ">" is replaced by "≥" if any two principal stretches are equal.…”

Section: Stochastic Isotropic Incompressible Hyperelastic Modelsmentioning

confidence: 99%

“…Radial oscillations of cylindrical tubes and spherical shells of neo-Hookean [102], Mooney-Rivlin [69,82], and Gent [32] hyperelastic materials were analysed in [15,16], where it was inferred that, in general, both the amplitude and period of oscillations decrease when the stiffness of the material increases. The influence of material constitutive law on the dynamic behaviour of cylindrical and spherical shells was also examined in [8,10,84,110], where the results for Yeoh [109] and Mooney-Rivlin material models were compared. In [19], the static and dynamic behaviour of circular cylindrical shells of homogeneous isotropic incompressible hyperelastic material modelling arterial walls were considered.…”

Section: Introductionmentioning

confidence: 99%

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Likely oscillatory motions of stochastic hyperelastic solids

Mihai

Fitt

Woolley

et al. 2019

Transactions of Mathematics and Its Applications

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Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as "likely oscillatory motions".Key words: stochastic hyperelastic models, dynamic finite strain deformation, quasi-equilibrated motion, finite amplitude oscillations, incompressibility, applied probability."Denominetur motus talis, qualis omni momento temporis t praebet configurationem capacem aequilibrii corporis iisdem viribus massalibus sollicitati, 'motus quasi aequilibratus'. Generatim motus quasi aequilibratus non congruet legibus dynamicis et proinde motus verus corporis fieri non potest, manentibus iisdem viribus masalibus." -C. Truesdell (1962) [103]

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“…In ( 9)- (10), the strict inequality ">" is replaced by "≥" if any two principal stretches are equal.…”

Section: Stochastic Isotropic Incompressible Hyperelastic Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Likely oscillatory motions of stochastic hyperelastic solids

Mihai

Fitt

Woolley

et al. 2019

Transactions of Mathematics and Its Applications

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“…A visco-hyperelastic model was presented by Zhao et al [141] for modelling the chaotic motion of spherical shells. Other studies on the dynamic behaviour of hyperelastic plates and shells can be found in refs [142][143][144][145][146][147][148], emphasising the importance of considering hyperelasticity in studying the dynamic response of such structures. Studies on the nonlinear dynamics of hyperelastic plates and shells are summarised in Table 2.…”

Section: Nonlinear Dynamics Of Hyperelastic Plates and Shellsmentioning

confidence: 99%

A review on the nonlinear dynamics of hyperelastic structures

et al. 2022

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This paper presents a critical review of the nonlinear dynamics of hyperelastic structures. Hyperelastic structures often undergo large strains when subjected to external time-dependent forces. Hyperelasticity requires specific constitutive laws to describe the mechanical properties of different materials, which are characterised by a nonlinear relationship between stress and strain. Due to recent recognition of the high potential of hyperelastic structures in soft robots and other applications, and the capability of hyperelasticity to model soft biological tissues, the number of studies on hyperelastic structures and materials has grown significantly. Thus, a comprehensive explanation of hyperelastic constitutive laws is presented, and different techniques of continuum mechanics, which are suitable to model these materials, are discussed in this literature review. Furthermore, the sensitivity of each hyperelastic strain energy density function to coefficient variation is shown for some well-known hyperelastic models. Alongside this, the application of hyperelasticity to model the nonlinear dynamics of polymeric structures (e.g., beams, plates, shells, membranes and balloons) is discussed in detail with the assistance of previous studies in this field. The advantages and disadvantages of hyperelastic models are discussed in detail. This present review can stimulate the development of more accurate and reliable models.

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“…Wang and Zhu [26] investigated the nonlinear vibrations of a hyperelastic beam under time-varying axial loading are derived via the extended Hamilton's principle. Iglesias et al [27] studied the large-amplitude axisymmetric free vibration of an incompressible hyperelastic orthotropic cylinder, and analyzed the influence of initial conditions, structural and material parameters on the dynamic behavior. With the Gent-Gent hyperelastic model, Alibakhshi and Heidari [28] researched the nonlinear vibration of a dielectric elastomer balloon considering the strain hardening and the second invariant of the Cauchy-Green deformation tensor, and found that the second invariant parameter could suppress the chaotic motion of the system.…”

Section: Introductionmentioning

confidence: 99%