Over the past 25 years ternary hard coatings produced by chemical vapor deposition (CVD) have played an increasingly important role in many applications, e.g. in machining and in the automotive and aerospace industries. A group of important representatives of this class of material are titanium aluminium nitride (TiAlN) systems, which age harden at elevated temperatures due to spinodal decomposition of TiAlN into TiN and cubic AlN. In order to describe the energetic balance and kinetics of the decomposition of supersaturated Ti(1-x)AlxN the strain energy density (SED) associated with this transformation must be known. In the present work this SED is evaluated by treating the three-phase system as a composite consisting of two types of transforming particles (TiN, AlN) embedded in a matrix (TiAlN) or as a random three-phase material. Under these assumptions, the analytical and numerical methods of continuum micromechanics can be brought to bear on the problem, the emphasis being put on Finite-Element-based unit cell methods in the present case. Cube-shaped volume elements consisting of a predefined number of periodic, nonoverlapping, equally sized, spherical particles embedded in a matrix were generated by a Random Sequential Insertion technique. Periodicity boundary conditions were applied to these unit cells and the Finite ElementMethod (FEM) was used to obtain the elastic fields due to transformation strains prescribed to the particles. These fields, in turn, allowed evaluating the SED of the transformed system. Primarily, effects of the Al mole fraction, of the volume fractions of the particles and of the macroscopic constraints (unconstrained, fully constrained, layer-constrained) on the SED were studied. In addition, results were obtained for particles of polyhedral shape and for voxel-type random phase arrangements. The predictions of the FEM-based periodic homogenization show that the SED is most strongly determined by the volume fraction of transformed material, by the Al mole fraction and by the microtopology of the volume elements used. In the case of matrix-inclusion topologies, the influence of the particle shape turned out to be rather small. Excellent agreement with analytical Transformation Field Analysis models based on Mori-Tanaka methods was achieved when using matrix-inclusion microtopologies, thus verifying previous modeling work. This good agreement was traced to the low elastic contrast of the constituents of the TiAlN-TiN-AlN system.