Spectral method for time-strain separable integral constitutive models in oscillatory shear

The time-strain separable Kaye–Bernstein–Kearsley–Zappas model (tssKBKZM) is a popular integral constitutive equation that used to the nonlinear response of materials using only their linear viscoelastic properties and damping function. In oscillatory shear, numerical evaluation tssKBKZM complicated by infinite domain integration, nature integrand. To avoid these problems, spectrally accurate method proposed. It approximates portion integrand discrete Fourier series, which enables analytical resulting integrals for Maxwell model. spectral generalized arbitrary continuous relaxation spectra. Upper bounds quadrature error, can often be driven machine precision, are presented. Doi–Edwards with independent-alignment approximation (DE-IA) special case tssKBKZM; DE-IA, compared trapezoidal rule highlight its accuracy efficiency. superiority proposed particularly evident at large strain amplitude frequency. For spectra, transforms double corresponding single integral. Solutions computed specified level standard libraries show typically two three orders magnitude faster. Extensions fractional rheological models, nonzero equilibrium modulus, stretched exponential etc., also discussed.