We introduce a novel approach for calculating the mechanical relaxation pattern of incommensurate bilayers over configuration space, bypassing the need for the standard supercell approximation and giving a true aperiodic structure. The model can be used for a wide variety of materials via use of a continuum model for intralayer interactions and the generalized stacking fault energy for interlayer interactions. The method extends the computationally accessible regime of weakly coupled bilayers with similar orientations and size, for example materials with a small relative twist where the widely studied large-scale moire patterns arise.