The method of harmonic balance for the Giesekus model under oscillatory shear

The method of harmonic balance (HB) is a spectrally accurate used to obtain periodic steady state solutions dynamical systems subjected perturbations. We adapt HB solve for the stress response Giesekus model under large amplitude oscillatory shear (LAOS) deformation. transforms system differential equations set nonlinear algebraic in Fourier coefficients. Convergence studies find that difference between and true decays exponentially with number harmonics (H) included ansatz as e−mH. decay coefficient m decreases increasing strain amplitude, exhibits “U” shaped dependence on applied frequency. computational cost increases slightly faster than linearly H. net result rapid convergence modest increase H implies outperforms conventional using numerical integration constitutive shear. Numerical experiments simultaneously about three orders magnitude cheaper, several more integration. Thus, it offers compelling value proposition parameter estimation or selection.