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

摘要

We introduce a fast numerical method for the evaluation of the effective elastic energy in martensitic polycrystals in two and three dimensions. The overall complexity of the method is (N) operations, where N is the number of component crystallites. Upper and lower bounds On the energy are also presented which allow us to estimate the accuracy of the numerical results. Our new three-dimensional computations and bounds for rando111 polycrystals, which are the first ones available in the literature, provide substantial insights on the behavior of polycrystalline martensites. They suggest that recoverable strains can be much larger than those attainable with zero energy.