Axisymmetric indentation of curved elastic membranes by a convex rigid indenter

@article{Pearce2011AxisymmetricIO,
  title={Axisymmetric indentation of curved elastic membranes by a convex rigid indenter},
  author={Simon P. Pearce and John R. King and M. J. Holdsworth},
  journal={International Journal of Non-Linear Mechanics},
  year={2011},
  volume={46},
  pages={1128 - 1138}
}
Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load–indentation curves that result for a range of spheroidal tips are obtained for both flat and curved membranes. Wrinkling may occur… 
Modeling the indentation and puncturing of inflated elastic membranes by rigid indenters
Abstract In this paper energy argument and maximum local deformation criteria are used to predict the puncturing of inflated elastic membranes by a rigid indenter. The direct membrane theory and a
Finite indentation of highly curved elastic shells
TLDR
The effect of bending stiffness is introduced, ensuring that energy is required to change the shell shape without stretching, and find that commonly neglected terms in the shell equilibrium equation must be included.
D ec 2 01 6 Finite indentation of highly curved elastic shells
Experimentally measuring the elastic properties of a thin-walled curved flexible biological surface is difficult. One technique which may be used is the indentation of a thin sheet of material by a
Indentation mapping of stretched adhesive membranes
Unilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson–Kendall–Roberts (JKR)-type and Derjaguin–
Tension of a cylindrical membrane partially stretched over a rigid cylinder
Abstract We study a contact problem with friction for a hyperelastic long thin-walled tube. One end of the tube is placed over an immovable, rough, rigid cylinder and an axial force is applied to
Puncture mechanics of soft elastomeric membrane with large deformation by rigid cylindrical indenter
Abstract Soft elastomeric membrane structures are widely used and commonly found in engineering and biological applications. Puncture is one of the primary failure modes of soft elastomeric membrane
Scaling laws and snap-through events in indentation of perforated membranes
Abstract We revisit the classical theory of indentation for very soft materials. Many experiments consist in extracting the stiffness of a membrane from the cubic answer of the force versus
Indentation of ellipsoidal and cylindrical elastic shells.
TLDR
It is shown that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth, revealing how geometry rules the rigidity of shells.
Finite inflation of a hyperelastic toroidal membrane over a cylindrical rim
The present paper is devoted to the study of finite inflation of a hyperelastic toroidal membrane on a cylindrical rim under uniform internal pressure. Both compliant and rigid frictionless rims have
Analytical, numerical and experimental analysis of continuous indentation of a flat hyperelastic circular membrane by a rigid cylindrical indenter
Abstract Several researchers have studied the process of the indentation of a membrane by rigid objects, but there is currently a lack of continuous indentation studies and experimental data to
...
1
2
3
...

References

SHOWING 1-10 OF 42 REFERENCES
Analysis of pulled axisymmetric membranes with wrinkling
The nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed. The membrane is considered to be ideal in the sense that it cannot carry compressive stress
Spherical indentation of freestanding circular thin films in the membrane regime
Abstract We present theoretical and experimental results to describe the mechanics of indentation of a clamped circular membrane with a frictionless spherical indenter. Analytical expressions and
Modeling the indentation, penetration and cavitation of elastic membranes
An energy argument is used to predict the penetration of an elastic membrane by a rigid cylindrical indenter. We study a sequence of axisymmetric equilibrium deformations beginning with the
Axisymmetric elastic membranes subjected to fluid loading
We consider axisymmetric isotropic elastic membranes that are loaded by an incompressible liquid. The resulting deformation which contains the liquid is assumed to be axisymmetric. We consider
Puncturing a thin elastic sheet
Abstract We use membrane theory to analyze the puncturing of a thin solid circular isotropic elastic sheet by a rigid axisymmetric indenter. A solution is obtained in which a hole is formed at the
Wrinkling on stretched circular membrane under in-plane torsion:
Abstract Wrinkling on a stretched circular membrane under in-plane torsion is a typical and classical problem in the study of wrinkling on membrane structures. This paper presents the experiment and
Point loads on a hemispherical elastic membrane
We analyze axisymmetric equilibrium deformations of a pressurized, hemispherical, isotropic elastic membrane subjected to a concentrated force at its pole. Wrinkling of the membrane is taken into
Decohesion of a rigid punch from non-linear membrane undergoing finite axisymmetric deformation
Abstract Adhesion of flexible thin film or membrane plays an important role in many biological and industrial applications. In many physical systems, large deformation is often expected, especially
Deflections of a rubber membrane
Abstract This paper deals with the problem of the transverse deflection of a natural rubber membrane that is fixed along a circular boundary. Uniaxial experiments were performed in order to
Large deformation possible in every isotropic elastic membrane
  • P. M. Naghdi, P. Tang
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1977
This paper is concerned with static solutions of finitely deformed elastic membranes regarded as thin shells. It deals with deformations that can be maintained, in the absence of body force, in every
...
1
2
3
4
5
...