Numerical simulation of martensitic transformations in two- and three-dimensional polycrystals

We introduce a fast numerical method for the evaluation of the effective el astic energy in martensitic polycrystals in two and three dimensions. The o verall complexity of the method is O(N) operations, where N is the number o f component crystallites. Upper and lower bounds on the energy are also pre sented which allow us to estimate the accuracy of the numerical results. Ou r new three-dimensional computations and bounds for random polycrystals, wh ich are the first ones available in the literature, provide substantial ins ights on the behavior of polycrystalline martensites. They suggest that rec overable strains can be much larger than those attainable with zero energy. (C) 2000 Elsevier Science Ltd. All rights reserved.