  Implicit-explicit (IMEX) time integration schemes are well suited for
nonlinear structural dynamics because of their low computational cost and high
accuracy. However, stability of IMEX schemes cannot be guaranteed for general
nonlinear problems. In this article, we present a scalar auxiliary variable
(SAV) stabilization of high-order IMEX time integration schemes that leads to
unconditional stability. The proposed IMEX-BDFk-SAV schemes treat linear terms
implicitly using kth-order backward difference formulas (BDFk) and nonlinear
terms explicitly. This eliminates the need for iterations in nonlinear problems
and leads to low computational cost. Truncation error analysis of the proposed
IMEX-BDFk-SAV schemes confirms that up to kth-order accuracy can be achieved
and this is verified through a series of convergence tests. Unlike existing SAV
schemes for first-order ordinary differential equations (ODEs), we introduce a
novel SAV for the proposed schemes that allows direct solution of the
second-order ODEs without transforming them to a system of first-order ODEs.
Finally, we demonstrate the performance of the proposed schemes by solving
several nonlinear problems in structural dynamics and show that the proposed
schemes can achieve high accuracy at a low computational cost while maintaining
unconditional stability.
