A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

TL;DR

This paper introduces a comprehensive hyperbolic model for nonlinear earthquake fault processes, capturing complex geometries, damage, and multi-physics interactions, enabling advanced simulations of dynamic rupture phenomena.

Contribution

It presents a unified, thermodynamically compatible hyperbolic model that incorporates nonlinear elasto-plasticity, damage, and viscous flows with complex fault geometries using diffuse interface methods.

Findings

Successfully simulates secondary shear cracks during rupture

Models tensile fracture in Brazilian disc tests

Demonstrates convection in molten rock-like materials

Abstract

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities, and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function $\xi \in [0,1]$ that indicates the local level of material damage. The model also permits the representation of arbitrarily complex geometries via a diffuse interface approach based on the solid volume fraction function $\alpha \in [0,1]$. Neither of the two scalar fields $\xi$ and $\alpha$ needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). The model shares common features with phase-field approaches but substantially extends them. We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material.