  Harmonic balance (HB) is a popular Fourier-Galerkin method used in the
analysis of nonlinear vibration problems where dynamical systems are subjected
to periodic forcing. We adapt HB to find the periodic steady-state response of
nonlinear differential constitutive models subjected to large amplitude
oscillatory shear flow. By incorporating the alternating-frequency-time scheme
into HB, we develop a computer program called FLASH (acronym for Fast Large
Amplitude Simulation using Harmonic balance), which makes it convenient to
apply HB to any differential constitutive model. We validate FLASH by
considering two representative constitutive models, viz., the exponential
Phan-Thien Tanner model and a nonlinear temporary network model. In terms of
accuracy and speed, FLASH outperforms the conventional approach of solving
initial value problems by numerical integration via time-stepping methods often
by several orders of magnitude. We discuss how FLASH can be conveniently
extended for other nonlinear constitutive models, which opens up potential
applications in model calibration and selection, and stability analysis.
