Effect of curvature and anisotropy on the finite inflation of a hyperelastic toroidal membrane

Tamadapu, Ganesh; DasGupta, Anirvan

doi:10.1016/j.euromechsol.2014.02.006

Cited by 16 publications

(14 citation statements)

References 34 publications

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“…To verify the authenticity of the formulation presented earlier, a comparison of our results with those obtained by Tamadapu and DasGupta (2014a) for free inflation of a purely elastic toroidal membrane is made. Figure 4 shows the comparison of the principal stretches (λ 1 , λ 2 ) and the non-dimensional Cauchy stresses (σ θ , σ φ ) where an appreciable matching of the numerical values can be seen.…”

Section: Validating the Formulationmentioning

confidence: 99%

“…We note the departure from the purely elastic case in which wrinkling usually tends to occur at the inner edge (Tamadapu and DasGupta, 2014a).…”

Section: Limit Pointsmentioning

confidence: 99%

“…Only non-dimensional quantities are used henceforth. We use the same values of the material parameter and magnetic susceptibility in our calculations that were used by Tamadapu and DasGupta (2014a) and Barham et al (2008) and are listed in Table 1.…”

Section: Cauchy Stressesmentioning

confidence: 99%

“…We attribute this behaviour to the geometrical properties inherent to a toroid. See (Tamadapu and DasGupta, 2014a) for a brief explanation of such a geometrical connection. Table 2: Comparison of the circular cross-section assumption with the general deformation for purely elastic case (M = 0).…”

Section: Comparison Of General and Parametric Deformationsmentioning

confidence: 99%

“…An instance of finite element approach for large deformations can be found in a recent study by Papargyri-Beskou (2005). Tamadapu and DasGupta (2012, 2014a have worked on inflation of incompressible toroidal membranes in which they also proposed directly integrating the system of second order ordinary differential governing equations. The boundary value problem is converted to an initial value problem by employing shooting method and a solution for the resulting problem is searched using Nelder-Meads optimization technique.…”

Section: Introductionmentioning

confidence: 99%

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Limit points in the free inflation of a magnetoelastic toroidal membrane

Reddy

Saxena

2017

International Journal of Non-Linear Mechanics

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One common phenomenon native to inflation of membranes is the elastic limit-point instability-a bifurcation point at which the membrane begins to deform enormously at the slightest increase of pressure. In the case of magnetoelastic materials, there is another possible phenomenon which we call magnetic limitpoint instability, a state referring to the non-existence of an equilibrium state -either stable or unstable. In this work, we are concerned with such instabilities in an incompressible isotropic magnetoelastic toroidal membrane with an initial circular cross-section. A non-uniform magnetic field is generated using a circular current carrying loop placed inside the membrane in addition to inflation by a uniform hydrostatic pressure. An energy formulation based on magnetization is used to model the magneto-mechanical coupling along with a Mooney-Rivlin constitutive model for the elastic strain energy density. Computations show that the magnetic field strongly influences the location of elastic limit points and in some cases can cause them to vanish. Multiple equilibrium states are obtained as solutions of the governing equations and a criterion based on second variation is employed to determine their stability. Existence and dependence of magnetic limit point on the magnetic field is demonstrated. While the quantitative results obtained here are specific to the toroidal geometry, the deformation behaviour can be generalised to any magnetoelastic membrane.

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Section: Validating the Formulationmentioning

confidence: 99%

“…We note the departure from the purely elastic case in which wrinkling usually tends to occur at the inner edge (Tamadapu and DasGupta, 2014a).…”

Section: Limit Pointsmentioning

confidence: 99%

Section: Cauchy Stressesmentioning

confidence: 99%

Section: Comparison Of General and Parametric Deformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Limit points in the free inflation of a magnetoelastic toroidal membrane

Reddy

Saxena

2017

International Journal of Non-Linear Mechanics

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Toward Development of Inflatable Stents with Application in Endovascular Treatments

Moghadam

Alaie

Gharaie

et al. 2018

Adv Funct Materials

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Although design and fabrication of metallic stents are extensively explored and established, the application of inflatable stents in endovascular treatments is relatively new. Inflatable stents introduce several advantages, such as repositionability and conformability to surrounding anatomic structures. These characteristics make the stent suitable for transcatheter treatment of cardiovascular diseases, such as valvular heart disease, and aortic aneurysms. This paper reports on a rapid and cost‐effective fabrication method, based on soft robotic technology, for the development of inflatable stents made of thermoplastic polyurethane. The stent is an inflatable cylinder that contains an array of bonded regions that form a continuous network, resembling a hexagonal lattice pattern. This pattern prevents the stent from buckling into an irregular shape upon inflation. The effect of this pattern on the maximum burst pressure, thickness, and pull‐out force of the stent is characterized. Finally, a trileaflet polyurethane valve is integrated into the inflatable stent frame to demonstrate its application as a transcatheter heart valve. This work serves as a proof of principle that inflatable stents can be useful in cardiovascular applications where conformability to surrounding tissue is advantageous, such as abdominal aortic aneurysm and aortic valve replacement.

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An Anisotropic Hyperelastic Inflated Toroidal Membrane in Lateral Contact with Two Flat Rigid Plates

Sahu

Roychowdhury

2022

Acta Mech. Solida Sin.

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Effect of curvature and anisotropy on the finite inflation of a hyperelastic toroidal membrane

Cited by 16 publications

References 34 publications

Limit points in the free inflation of a magnetoelastic toroidal membrane

Limit points in the free inflation of a magnetoelastic toroidal membrane

Toward Development of Inflatable Stents with Application in Endovascular Treatments

An Anisotropic Hyperelastic Inflated Toroidal Membrane in Lateral Contact with Two Flat Rigid Plates

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