## Brittany A. Erickson (08/08/16)

Math Colloquium

### Speaker: Brittany A. Erickson

Title: A Finite Difference Method for Plastic Response with an Application to the Earthquake Cycle

Location: V-157, VR-II.

Time: Monday, August 8 at 13:20.

### Abstract:

We are developing an efficient, computational framework for simulating multiple earthquake cycles with off-fault plastic response. Both rate-independent and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The constitutive theory furnishes a nonlinear elliptic partial differential equation which must be solved through an iterative procedure. A frictional fault lies at an interface in the domain. The off-fault volume is discretized using finite differences satisfying a summation-by-parts rule and interseismic loading is accounted for at the remote boundaries through weak enforcement of boundary conditions. Time-stepping is done through an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm to obtain stresses consistent with the constitutive theory. Solutions are verified by convergence tests along with comparison to a finite element solution. I will conclude with some application problems related to earthquake cycle modeling.