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