  We present a practical algorithm for partially relaxing multiwell energy
densities such as pertain to materials undergoing martensitic phase
transitions. The algorithm is based on sequential lamination, but the evolution
of the microstructure during a deformation process is required to satisfy a
continuity constraint, in the sense that the new microstructure should be
reachable from the preceding one by a combination of branching and pruning
operations. All microstructures generated by the algorithm are in static and
configurational equilibrium. Owing to the continuity constrained imposed upon
the microstructural evolution, the predicted material behavior may be
path-dependent and exhibit hysteresis. In cases in which there is a strict
separation of micro and macrostructural lengthscales, the proposed relaxation
algorithm may effectively be integrated into macroscopic finite-element
calculations at the subgrid level. We demonstrate this aspect of the algorithm
by means of a numerical example concerned with the indentation of an Cu-Al-Ni
shape memory alloy by a spherical indenter.
