Elastic Landau states as martensite nuclei in austenite

In this article, we investigate the geometric closure of austenite--martensite interfaces. Classical compatibility conditions permit stress-free interfaces between the two phases: the condition λ₂ = 1 admits planar interfaces, whereas the cofactor conditions additionally admit curved interfaces. However, neither, guarantees the geometric closure of these interfaces. We identify two-parameter families of martensitic deformations that overcome this limitation and enable the formation of closed, stress-free martensite nuclei embedded in an austenite matrix. A main result is the interpretation of the classical deformation modes of simple shear and pure shear as martensitic phase transformations. These correspond to cubic to monoclinic-II and cubic to orthorhombic transformations, respectively. The former naturally satisfies the extreme compatibility conditions, which are stronger than the cofactor conditions, and gives rise to elastic Landau states, a self-accommodating martensitic nuclei embedded in austenite. We show that these states can be assembled to form arbitrarily shaped, stress-free martensitic islands surrounded by austenite. Such states can arise even in conventional shape memory alloys that do not satisfy supercompatibility, provided hierarchical twinning produces an average deformation that is a simple shear. The theory provides a geometric mechanism for self-accommodation. Its predicted deformation gradients agree with those reconstructed from experimentally observed microstructures. This agreement suggests that these microstructures originate from simple shear.