Geometrical feature of the scaling behavior of the limit-point pressure of inflated hyperelastic membranes

Abstract

The occurrence of the limit-point instability is an intriguing phenomenon observed during stretching of hyperelastic membranes. In toy rubber balloons, this phenomenon may be experienced in the sudden reduction in the level of difficulty of blowing the balloon accompanied by its rapid inflation. The present paper brings out a link between the geometry and strain-hardening parameter of the membrane, and the occurrence of the limit-point instability. Inflation of membranes with different geometries and boundary conditions is considered, and the corresponding limit-point pressures are obtained for different strain-hardening parameter values. Interestingly, it is observed that the limit-point pressure for the different geometries is inversely proportional to a geometric parameter of the uninflated membrane. This dependence is shown analytically, which can be extended to a general membrane geometry. More surprisingly, the proportionality constant has a power-law dependence on the nondimensional material strain-hardening parameter. The constants involved in the power-law relation are universal constants for a particular membrane geometry.

Free and constrained inflation of a pre-stretched cylindrical membrane

“…Recently, Patil & DasGupta [23] demonstrated a stretch-induced softening/stiffening phenomenon during free inflation of unstretched and prestretched hyperelastic circular flat membranes. The geometry-dependent scaling behaviour of the limit point pressure is uncovered by Tamadapu et al [24]. Over the past four decades, many researchers have studied the membrane contact problems, largely with frictionless contact, in various contexts and for different geometries [25][26][27][28][29].…”

Finite Inflation Analysis of Two Circumferentially Bonded Hyperelastic Circular Flat Membranes

“…3(a)) due to a stretch induced softening. The nature of the limit point and its intriguing relation to the geometry and the strain hardening parameter oq has been shown recently [50]. For two bonded identical membranes (oci = a2 = a (say), a3 = 1), it has been found that the limit point pressure is given by (see Ref. [50]) f W = a (l + a)6…”

“…In this connection, it has been recently shown in Ref. [50] that the limit point instability pressure is related to the characteristic dimension (radius) of the undeformed structure, and the strain hardening parameter of the membrane through two universal constants of the geometry. We explore the connection of the limit point pressure with the observed phenomenon.…”

Coupled electro-elastic deformation and instabilities of a toroidal membrane

“…This phenomenon is also called snap-through bifurcation and has been well studied [see e.g. 7,10,29,52,70]. Computation of accurate pressure-volume characteristics in this case require a path-following scheme due to the non-uniqueness of solution [59].…”