Stresses in lipid membrane models

The stresses in a membrane model are significant for two reasons. One is that the model-dependent tractions on the surface directly generate the external fluid velocity field in the boundary integral representation of Stokes flows. Another is that the nature of the stresses may or may not be compatible with constitutive restrictions on the membrane itself, such as fluidity. A fluid constitutive model restricts dependence on a referential configuration to information about change in area, and is often presumed to preclude static shear stresses. Geometric bending energies, such as those based on mean curvature, are not as simple as one might assume, as they inherently couple bending and tangential stresses. For this reason, Helfrich-like energies generate shear stresses, despite being fluid, as the deviatoric part of the bending tensor leads to a corresponding deviatoric part of the stress tensor. By contrast, the correct continuum limit of a Seung-Nelson-like bending energy produces a stress with purely isotropic tangential part, despite not being fluid.