Discontinuous deformation analysis (DDA) is a discrete element method that was developed for computing large deformation in fractured rock masses. In this paper we present details of the DDA time integration scheme, where the acceleration is taken constant over the time step, equal to the acceleration at the end of the time step (“right Riemann”). The integration scheme has several advantages: (1) Self-starting, (2) accelerations never need to be computed which reduces implementation complexity, (3) unconditionally stable, and (4) dissipative, contains algorithmic damping which may be important considering the penalty formulation of DDA. However, the right Riemann scheme is implicit, requiring expensive factorization or iteration to solve the resulting system of equations, and is accompanied by a bifurcation in the spectrum when the time step is large with respect to the period. This bifurcation has important ramifications for controlling spurious resonance in DDA simulations due to linear scaling in system stiffness compared to cubic scaling of the system mass as the characteristic length of the domain increases.
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Time Integration in Discontinuous Deformation Analysis
Journal of Engineering MechanicsOctober 2002
Journal of Engineering MechanicsAugust 2002
Journal of Engineering MechanicsMay 2007
Journal of Engineering MechanicsAugust 2008
Postdoctoral Researcher, Civil and Environmental Engineering, Univ. of California Berkeley, 2108 Shattuck Ave., Berkeley, CA 97420-1716.
Professor, Civil and Environmental Engineering, Univ. of California Berkeley, 2108 Shattuck Ave., Berkeley, CA 97420-1716.
Received: March 28, 2003
Accepted: August 18, 2003
Published online: February 19, 2004
Copyright © 2004 American Society of Civil Engineers