Instability of equilibrium of evolving laminates in pseudo-elastic solids

► Laminated microstructures evolve with rate-independent dissipation. ► We perform systematic analysis of stability of phase-transforming laminates. ► We prove that intrinsic instability of an infinitely fine laminate is a rule. ► Elastic micro-strain energy is shown to stabilize laminates of finite spacing. ► Illustrative examples are provided for a CuZnAl shape memory alloy.