The Landau potential for multivariant displacive phase transformations (PTs) is derived for the most general case of large rotations, elastic and transformational strains, as well as nonlinear and different elastic properties of phases. The method of repetitive superposition of large strains is extended for PTs and is utilized in the finite-element method approach for solution of corresponding coupled phase-field and mechanical problems. Problems of martensitic variants nucleation and evolution in a nanosize sample, including a sample with two nanovoids, are solved. A similar approach can be applied for twinning, dislocations, and reconstructive PTs.