Abstract
A boundary-value problem is formulated describing the shapes of inflated and deflated axisymmetric capsules enclosed by elastic membranes. When the membrane tension is isotropic and the principal bending moments obey constitutive equations involving the principal curvatures in the reference and deformed state but not the stretch ratios, the capsule shape is governed by a third-order ordinary differential equation for the meridional curvature involving the difference between the internal and external pressure. Numerical solutions of the boundary-value problem illustrate the shape of deflated spherical capsules enclosed by incompressible membranes and the shape of inflated and deflated biconcave capsules resembling red blood cells. The results demonstrate that the solution space of deformed spherical capsules consists of bifurcating branches arising at a sequence of transmural pressures, and illustrate the pressure developing inside spherical and biconcave capsules when a certain amount of fluid has been injected into, or withdrawn from, the interior.
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Pozrikidis, C. Deformed shapes of axisymmetric capsules enclosed by elastic membranes. Journal of Engineering Mathematics 45, 169–182 (2003). https://doi.org/10.1023/A:1022154201045
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DOI: https://doi.org/10.1023/A:1022154201045