  A chemo-mechanical model for a finite-strain elasto-viscoplastic material
containing multiple chemical components is formulated and an efficient
numerical implementation is developed to solve the resulting transport
relations. The numerical solution relies on inverting the constitutive model
for the chemical potential. In this work, a semi-analytical inversion for a
general family of multi-component regular-solution chemical free energy models
is derived. This is based on splitting the chemical free energy into a convex
contribution, treated implicitly, and a non-convex contribution, treated
explicitly. This results in a reformulation of the system transport equations
in terms of the chemical potential rather than the composition as the
independent field variable. The numerical conditioning of the reformulated
system, discretised by finite elements, is shown to be significantly improved,
and convergence to the Cahn-Hilliard solution is demonstrated for the case of
binary spinodal decomposition. Chemo-mechanically coupled binary and ternary
spinodal decomposition systems are then investigated to illustrate the effect
of anisotropic elastic deformation and plastic relaxation of the resulting
spinodal morphologies in more complex material systems.
