Kramers–Kronig relations for nonlinear rheology. Part I: General expression and implications

The principle of causality leads to linear Kramers–Kronig relations (KKR) that relate the real and imaginary parts complex modulus [Formula: see text] through integral transforms. Using multiple generalization Boltzmann superposition for nonlinear rheology, causality, we derived KKR, which order text]. For text], obtained KKR medium amplitude parallel (MAPS) rheology. A special case MAPS is oscillatory shear (MAOS); MAOS third-harmonic text]; however, no such exists first harmonic We verified single mode Giesekus model. also probed sensitivity when domain integration truncated a finite frequency window. found (i) inferring from more reliable than vice versa, (ii) predictions over particular range require approximately an excess one decade data beyond prediction, (iii) particularly susceptible errors at large frequencies.