  The deformation-related energy budget is usually considered in the simplest
form or even completely omitted from the energy balance equation. We derive a
full energy balance equation that accounts not only for heat energy but also
for mechanical (elastic, plastic and viscous) work. The derived equation is
implemented in DES3D, an unstructured finite element solver for long-term
tectonic deformation. We verify the implementation by comparing numerical
solutions to the corresponding semi-analytic solutions in three benchmarks
extended from the classical oedometer test. Two of the benchmarks are designed
to evaluate the temperature change in a Mohr-Coulomb elasto-plastic square
governed by a simplified equation involving plastic power only and by the full
temperature evolution equation, respectively. The third benchmark differs in
that it computes thermal stresses associated with a prescribed uniform
temperature increase. All the solutions from DES3D show relative error less
than 0.1%. We also investigate the long-term effects of deformation energetics
on the evolution of large offset normal faults. We find that the models
considering the full energy balance equation tend to produce more secondary
faults and an elongated core complex. Our results for the normal fault system
confirm that persistent inelastic deformation has a significant impact on the
long-term evolution of faults, motivating further exploration of the role of
the full energy balance equation in other geodynamic systems.
