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The deformation-related energy budget is usually considered in the simplestform or even completely omitted from the energy balance equation. We derive afull energy balance equation that accounts not only for heat energy but alsofor mechanical (elastic, plastic and viscous) work. The derived equation isimplemented in DES3D, an unstructured finite element solver for long-termtectonic deformation. We verify the implementation by comparing numericalsolutions to the corresponding semi-analytic solutions in three benchmarksextended from the classical oedometer test. Two of the benchmarks are designedto evaluate the temperature change in a Mohr-Coulomb elasto-plastic squaregoverned by a simplified equation involving plastic power only and by the fulltemperature evolution equation, respectively. The third benchmark differs inthat it computes thermal stresses associated with a prescribed uniformtemperature increase. All the solutions from DES3D show relative error lessthan 0.1%. We also investigate the long-term effects of deformation energeticson the evolution of large offset normal faults. We find that the modelsconsidering the full energy balance equation tend to produce more secondaryfaults and an elongated core complex. Our results for the normal fault systemconfirm that persistent inelastic deformation has a significant impact on thelong-term evolution of faults, motivating further exploration of the role ofthe full energy balance equation in other geodynamic systems.

Incorporating Deformation Energetics in Long-Term Tectonic Modeling