Compression of a capsule: mechanical laws of membranes with negligible bending stiffness

The compression of a capsule between two plates is considered. The problem is solved numerically for a capsule made of an incompressible liquid drop surrounded by a thin elastic membrane which has a negligible bending stiffness. Numerical results are provided for three different mechanical laws of the membrane. By considering elastic moduli independent of the deformation, we show that the isotropic dilation plays the major role. In particular, an asymptotic behavior independent of the shear modulus is found for large deformations. For more complex models, the deformation limits beyond which the variation of elastic moduli starts to play a role are examined. The results indicate that the distinction between the different models requires a careful inspection of both small and large deformations. The theoretical predictions are compared with experimental results. For millimetric capsules with membranes made of covalently linked human serum albumin and alginate, the best agreement is obtained by considering that the elastic moduli are independent of the deformation and range from 0.1 to 4 N/m.