for the entire system is described as the sum of the contribution of all the discrete elements work components. For each discrete element the virtual work is determined by the force vector and the displacement vector each for an applied stress and a bending momentum The FE force vectors due to the applied bilayer stress are given as Here is the displacement state function at point , and the tangent vector to the bilayer surface at point The above individual element vectors for the internal force and the internal work can be expressed in a global assembly to obtain a discretized weak form as follows: In the above equation is the deformation in each discrete element while is the Lagrange multiplier associated with area-incompressibility. The discretized weak form is satisfied when and . The resulting nonlinear equations are solved using Newton ‘s method. This allows the predictions of equilibrium shapes that lipid membranes adopt under different stimuli. Most analysis are done for lipid membranes with uniform properties (isotropic), while this is partly true for simple membranes containing a single or few lipid species, this description can only approximate the mechanical response of more complex lipid bilayers which can contain several domains of segregated lipids having distinct material properties or intermembrane proteins as in the case of cellular membranes. Other complex cases requiring surface flow analysis, pH, and temperature dependency would require a more discrete model of a bilayer such as MD simulations. FE methods can predict the equilibrium conformations of a lipid bilayer in response to external forces as shown in the following cases. Tethering In this scenario a point in the bilayer surface is pulled with a force normal to the surface plane, this leads to the elongation of a thin tether of bilayer material. The rest of the bilayer surface is subject to a tension S reflecting the pulling force of the continuous bilayer. In such this case a finer mesh is applied near the pulling force area to have a more accurate prediction of the bilayer deformation. Tethering is an important mechanical event for cellular lipid bilayers, by this action membranes are able to mediate docking into substrates or components of the cytoskeleton. Budding Lipid bilayer budding is a commonplace phenomenon in living cells and relates to the transport of metabolites in the form of vesicles. During this process, a lipid bilayer is subject to internal hydrostatic