Skip to main content
A Finite Difference Method for Off-fault Plasticity throughout the Earthquake Cycle
Journal of the Mechanics and Physics of Solids
  • Brittany A. Erickson, Portland State University
  • Eric M. Dunham, Stanford University
  • Arash Khosravifar, Portland State University
Document Type
Publication Date
  • Earthquakes -- Mathematical models,
  • Finite differences,
  • Elastoplasticity -- Mathematical models

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiationdamping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic off-set is accommodated by inelastic deformation (~0.1 m per rupture, or ~10% of the tectonic deformation budget).


This is a PDF of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. -- From the publisher

This article has been released with a Creative Commons Attribution Non-Commercial No Derivatives License [CC BY-NC-ND 4.0]

Persistent Identifier
Citation Information
Brittany A. Erickson, Eric M. Dunham, Arash Khosravifar, A Finite Difference Method for Off-fault Plasticity throughout the Earthquake Cycle, Journal of the Mechanics and Physics of Solids (2017), doi: 10.1016/j.jmps.2017.08.002