On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elastodynamics

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Transient three‐dimensional domain decomposition problems: Frame‐indifferent mortar constraints and conserving integration (2010, background): “It is now well established that energy–momentum conserving time-stepping schemes (see e.g. Gonzalez [21, 22] and Betsch and Steinman [23, 24]) and energy-decaying variants thereof (see e.g. Armero and Romero [25, 26]) provide enhanced numerical stability for applications in nonlinear structural dyna”
Variational time integrators (2004, background): “The simulation of the dynamics of rotor blades and similar systems has long been a challenge and a test bed for time-integration algorithms for structural dynamics [38–43].”
An energy‐consistent material‐point method for dynamic finite deformation plasticity (2006, methodology): “The addition of a dissipation term D > 0 to the discrete derivative has been used previously in [4], [5] to add controllable high frequency dissipation to dynamic hyperelastic simulations.”