Measurements related to the indentation of a circular membrane can be used to characterize the material response of a wide variety of materials, including biological tissue. In this paper, the axisymmetric deformation of an initially planar, homogeneous and uniformly thin membrane that is supported along a circular boundary and indented by a spherical indenter is considered.
MofradMRKKammRD. Cytoskeleton Mechanics. Cambridge University Press, New York, 2006.
2.
DoshiNZahrASBhaskarSLahannJMitragotriS. Red blood cell-mimetic particles: Bridging the gap between synthetic and biological materials. Proc Nat Acad Sci2009; 106: 21495–21499.
3.
FengWWYangWH. On the contact problem of an inflated spherical nonlinear membrane. J Appl Mech1973; 40: 209–214.
4.
NadlerB. On the contact of a spherical membrane enclosing a fluid with rigid parallel planes. Int J Non-linear Mech2010; 45: 294–300.
5.
YangWHHsuKH. Indentation of a circular membrane. J Appl Mech1971; 38: 227–230.
6.
WinemanAS. Nonlinear viscoelastic membranes. Comp and Math with Appl2007; 53: 168–181.
7.
FungYC. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer, 1981.
8.
PipkinACRogersTG. A non-linear representation for viscoelastic behavior. J Mech and Phys Solids1968; 16: 59–72.
9.
GreenAEAdkinsJE. Large Elastic Deformations and Nonlinear Continuum Mechanics. Oxford University Press, 1960.