The self-consistent solution of the coupled fields of Eqs. ( ) and ( ) is achieved using a staggered iteration method for each time increment. This staggered iteration method allows the solution scheme of each field to be prescribed independently. The mechanical equilibrium equation, Eq. ( ), is solved using an inexact Newton method with a critical point secant line search . For the reaction-diffusion equation, Eq. ( ), the Newton method with a backtracking line search is employed. Within each Newton iteration for both equations, a flexible GMRES linear solver preconditioned with a smoothed-aggregation algebraic multigrid method is employed for the linear solve. The numerical solution procedure is described in detail in Liu et al. and Shanthraj et al. .