Michael Parks*, P. Lindsay, A. Prakash
*Sandia National Laboratories
Lyles School of Civil Engineering

A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics

Peridynamics is a nonlocal reformulation of continuum mechanics that is suitable for representing deformations with discontinuities, see [1, 2] and the references therein. We extend the peridynamic formulation to allow the use of multiple time steps within a single problem domain by decomposing that domain into a number of smaller subdomains, where the critical regions of interest are solved using a small time step and the rest of the problem domain is solved using a larger time step. We explore the numerical properties and computational cost of the proposed approach, and demonstrate through numerical examples that a multi-time-step discretization of peridynamics can be solved much faster than a uniform time step discretization, and without adversely affecting the accuracy of the computed solution [3].

[1] S. A. Silling, "Reformulation of elasticity theory for discontinuities and long-range forces", J. Mech. Phys. Solids, 48 175-209 (2000).
[2] S. Silling, M. Epton, O. Weckner, J. Xu, and E. Askari, "Peridynamic states and constitutive modeling", J. Elasticity, 88, 151-184 (2007).
[3] P. Lindsay, M.L. Parks, and A. Prakash, "Enabling fast, stable and accurate peridynamics computations using multi-time-step integration", Submitted, 2014.
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