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

TL;DR

This paper develops a comprehensive Eulerian model for poro-elastodynamics incorporating damage, inelastic strains, and fluid flow, aimed at geophysical applications in Earth's lithosphere, with a focus on mathematical consistency and energy conservation.

Contribution

It introduces a fully Eulerian formulation of poro-elastodynamics with damage and fluid flow, extending previous models for better analytical and physical consistency.

Findings

Derived energetics for the model ensuring energy conservation.

Proved existence of global weak energy-conserving solutions.

Completed previous models to be mechanically consistent and analytically tractable.

Abstract

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 in [V. Lyakhovsky et al., Pure Appl. Geophys., 171:3099-3123, 2014] and [V. Lyakhovsky et al., Izvestiya, Physics of the Solid Earth, 43:13-23, 2007] is completed to make it mechanically consistent and amenable for analysis.