  In this paper we consider nonlinearly elastic, frame-indifferent, and
singularly perturbed two-well models for materials undergoing solid-solid phase
transitions in any space dimensions, and we perform a simultaneous passage to
sharp-interface and small-strain limits. Sequences of deformations with
equibounded energies are decomposed via suitable Caccioppoli partitions into
the sum of piecewise constant rigid movements and suitably rescaled
displacements. These converge to limiting partitions, deformations, and
displacements, respectively. Whereas limiting deformations are simple laminates
whose gradients only attain two values, the limiting displacements belong to
the class of special functions with bounded variation (SBV). The latter feature
elastic contributions measuring the distance to simple laminates, as well as
jumps associated to two consecutive phase transitions having vanishing
distance, and thus not being detected by the limiting deformations. By
Gamma-convergence we identify an effective limiting model given by the sum of a
quadratic linearized elastic energy in terms of displacements along with two
surface terms. The first one is proportional to the total length of interfaces
created by jumps in the gradient of the limiting deformation. The second one is
proportional to twice the total length of interfaces created by jumps in the
limiting displacement, as well as by the boundaries of limiting partitions. A
main tool of our analysis is a novel two-well rigidity estimate which has been
derived in [32] for a model with anisotropic second-order perturbation.
