  This paper discusses the free energy of complex dislocation microstructures,
which is a fundamental property of continuum plasticity. In the past, multiple
models of the self energy of dislocations have been proposed in the literature
that partially contradict each other. In order to gain insight into the
relationship between dislocation microstructures and the free energy associated
with them, instead of deriving a model based on theoretical or phenomenological
arguments, here, these quantities are directly measured using large scale
molecular dynamics simulations. Plasticity is induced using nanoindentation
that creates an inhomogeneous distribution of dislocations as the result of
dislocation nucleation and multiplication caused by the local deformation.
Using this approach, the measurements of dislocation densities and free
energies are ab-initio, because only the interatomic potential is defining the
reaction of the system to the applied deformation. The simulation results
support strongly a linear relation between the scalar dislocation density and
the free energy, which can be related very well to the classical model of
mechanical energy of straight dislocations, even for the complex dislocation
networks considered here.
