A convective model for poro-elastodynamics with damage and fluid flow towards Earth lithosphere modelling

Devised towards geophysical applications for various processes in the lithosphere or the crust, a model of poro-elastodynamics with inelastic strains and other internal variables like damage (aging) and porosity as well as with diffusion of water is formulated fully in the Eulerian setting. Concepts of gradient of the total strain rate as well as the additive splitting of the total strain rate are used while eliminating the displacement from the formulation. It relies on that the elastic strain is small while only the inelastic and the total strains can be large. The energetics behind this model is derived and used for analysis as far as the existence of global weak energy-conserving solutions concerns. By this way, the model of Lyakhovsky et al. (Appl Geophys 171:3099-3123, 2014; J Mech Phys Solids 59:1752-1776, 2011) is completed to make it mechanically consistent and amenable for analysis.

Automated summary

This model is developed for geophysical applications, considering inelastic strains, damage, porosity, and water diffusion in the lithosphere or crust. It uses concepts of total strain rate gradient and additive splitting while excluding displacement, making it mechanically consistent and analyzable. The energetics of the model are derived to analyze the existence of global weak energy-conserving solutions.