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We derive the expression of the stress tensor for one and two-component lipidmembranes with density and composition inhomogeneities. We first express themembrane stress tensor as a function of the free-energy density by means of theprinciple of virtual work. We then apply this general result to a monolayermodel which is shown to be a local version of the area-difference elasticity(ADE) model. The resulting stress tensor expression generalizes the oneassociated with the Helfrich model, and can be specialized to obtain the oneassociated with the ADE model. Our stress tensor directly gives the forceexchanged through a boundary in a monolayer with density and compositioninhomogeneities. Besides, it yields the force density, which is also directlyobtained in covariant formalism. We apply our results to study the forcesinduced in a membrane by a local perturbation.

Membrane stress tensor in the presence of lipid density and composition inhomogeneities