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A method to calculate the bending rigidity $\kappa$, saddle-splay modulus$\bar{\kappa}$, and spontaneous curvature $C_0$ of a fluid membrane isproposed. Virtual work for the bending deformations into cylindrical andspherical shapes is calculated for a flat membrane. This method does notrequire a force decomposition, unlike the existing stress-profile method. Thefirst derivative of the deformation gives $\kappa C_0$ and is a discrete formof the first moment of the stress profile. The second derivatives give $\kappa$and $\bar{\kappa}$, and include the variance terms of the first derivatives,which are not accounted for in the stress-profile method. This method isexamined for a solvent-free meshless membrane model and adissipative-particle-dynamics two-bead amphiphilic molecular model. It isconcluded that $\kappa$ and $\bar{\kappa}$ of a thin membrane can be accuratelycalculated, whereas for a thick membrane or one with an explicit solvent, afurther extension to include the volume-fluctuation effects is required for anaccurate estimation. The amplitude of the volume-fluctuation effects can beevaluated using the parameter dependence in the present method.

Virtual bending method to calculate bending rigidity, saddle-splay modulus, and spontaneous curvature of thin fluid membrane