# Incorporating Deformation Energetics in Long-Term Tectonic Modeling

## TL;DR

This paper develops a comprehensive energy balance equation for long-term tectonic modeling, incorporating heat and mechanical work, and demonstrates its implementation and effects on fault evolution in numerical simulations.

## Contribution

It introduces a full energy balance equation accounting for heat and mechanical work in tectonic models, implemented in DES3D, and explores its impact on fault system evolution.

## Key findings

- Models with full energy balance produce more secondary faults.
- Full energy considerations lead to elongated core complexes.
- Persistent inelastic deformation significantly affects fault evolution.

## Abstract

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.