Free and constrained inflation of elastic membranes in relation to thermoforming — non-axisymmetric problems

Abstract

This paper deals with the inflation of elastic membranes of general shapes in the context of thermoforming of heated polymeric sheets against relatively cold moulding surfaces. A previous paper (1) has dealt with axisymmetric problems. As before, both theoretical and experimental investigations are reported. The theoretical part consists of a self-contained finite element formulation for large deformation, free and constrained inflation of isotropic elastic membranes. The computer program developed on the basis of presented formulation is applied to free and constrained inflation of plane elliptical membranes of aspect ratios 2 and 4. The material model adopted is that of a single constant neo-Hookean elastic material. The constrained analyses are carried out for inflation against: (a) cylindrical walls (90 degree elliptical cones), (b) 60 degree elliptical cones, and (c) horizontal plates. Separate analyses are performed by assuming the contact to be either slipless or frictionless. The theoretical results are compared with the experimental ones for free inflation and constrained inflation cases (a) and (c).

Shear modulation of intercellular contact area between two deformable cells colliding under flow

“…The finite element implementation of the force F(x) calculation of the membrane is based on the model developed by (Charrier, et al, 1989) and (Shrivastava and Tang, 1993). The membrane is discretized into triangular finite elements to obtain the forces acting at the discrete nodes of the membrane surface, which are then distributed onto the fluid grid as described above.…”

Large deformation of red blood cell ghosts in a simple shear flow

“…Our finite element model of the membrane is based on the model developed by Charrier et al 32 and Shrivastava and Tang. 33 The model is used to obtain the forces acting at the discrete nodes of the membrane which are then distributed onto the fluid grid as described above.…”

“…Here we summarize the characteristics of the model and refer the reader to Refs. 32 and 33 for specific details. The capsule membrane is discretized into flat triangular elements which remain flat after deformation.…”

Limit points in the free inflation of a magnetoelastic toroidal membrane

“…Study of the mechanical behaviour of membranes should account for the nonlinearity in their geometry as well as the material models. Several extensive studies have been carried out, for example on the inflation of elastic membranes by Wineman (1976), Naghdi and Tang (1977), Fulton and Simmonds (1986), Khayat and Derdouri (1995), Jiang and Haddow (1995), Bonet et al (2000), Patil et al (2014), and on contact problems by Feng and Yang (1973), and Charrier et al (1989).…”