Three constitutive laws (Skalak et al.'s law extended to area-compressible interfaces, Hooke's law and the Mooney–Rivlin law) commonly used to describe the mechanics of thin membranes are presented and compared. A small-deformation analysis of the tension–deformation relation for uniaxial extension and for isotropic dilatation allows us to establish a correspondence between the individual material parameters of the laws. A large-deformation analysis indicates that the Mooney–Rivlin law is strain softening, whereas the Skalak et al. law is strain hardening for any value of the membrane dilatation modulus. The large deformation of a capsule suspended in hyperbolic pure straining flow is then computed for several membrane constitutive laws. A capsule with a Mooney–Rivlin membrane bursts through the process of continuous elongation, whereas a capsule with a Skalak et al. membrane always reaches a steady state in the range of parameters considered. The small-deformation analysis of a spherical capsule embedded in a linear shear flow is modified to account for the effect of the membrane dilatation modulus.

The transient deformation of an axisymmetric capsule freely suspended in a pure straining flow is studied, for sudden or periodic variations of the intensity of the rate of strain. The particle Reynolds number is supposed to be very small and the problem is solved numerically by means of the boundary integral method. In the case of a sudden start of flow, the time response of the capsule can be approximated by an exponential function, and is thus characterized by only two parameters: the equilibrium deformation D ϱ and the characteristic response time s. The respective influence of viscosity ratio, membrane elasticity, and initial particle geometry is analyzed. The dynamic response of the capsule subjected to periodic variations of the rate of strain is also studied. The response time s appears to be an appropriate parameter to estimate the capsule adaptability to changing flow conditions.

The role of membrane surface viscosity is investigated in the transient response of an axisymmetric capsule following a sudden start of external flow. Results obtained in a recent study for capsules with a hyperelastic membrane [Phys. Fluids 12, 948 (2000)] are extended to account for membrane viscosity. The common feature between hyperelastic and viscoelastic membranes is the time evolution of capsule deformation which can be fitted to an exponential function and thus characterized with only two parameters, the deformation at steady state D∞ and the response time τs. Membrane and bulk viscosity have quasilinear and independent effects on the transient response.