Theory of strain percolation in metals: mean field and strong boundary universality class

For the percolation model of strain in a deforming metal proposed earlier, we develop sum rule and mean field approximations which predict a critical point. The numerical work is restricted to the simpler of two cases proposed in the earlier work, in which the cell walls are “strong”, and unzipping of the dislocation entities which lock the walls into the lattice is not permitted. For this case, we find that strain percolation is a new form of correlated percolation, but that it is in the same universality class as standard percolation.