Virtual Forces

When virtual work theorem is used with a virtual force field and real deformations, the resulting method is called Virtual Force method. 'Virtual' in this context is simply 'not real', 'imaginary'. It is a device of convenience. The virtual force method can be conveniently applied to the problem at hand: calculation of displacements. The method of virtual forces is used often enough to be worth formally stating it here:

For a given structure, if a virtual (imaginary) equilibrium force field is considered with a real, geometrically compatible displacement field, then the Work Product, $\bar{W}$, of the external virtual forces and real displacements is equal to the work product, $\bar{U}$, of the internal, virtual stress resultants and real deformations.

To stress that the work products are calculated with virtual (imaginary) force field, we use a bar over U and W.

It is important to stress that the deformations are caused by whatever reason, not by virtual forces. Very often it is convenient to apply a virtual force of unit magnitude in units, consistent with the force and displacement units used in the calculation.

It is worth repeating that the deformations can be elastic, or plastic; they may be caused by temperature changes or any other cause. Even the displacements from the intended shape due to manufacturing inaccuracies can be calculated by the method of virtual forces. The only requirement in addition to geometrical consistency is that we can only deal with small displacements.