# How to define the storage and loss moduli for a rheologically nonlinear material?

## TL;DR

This paper explores how to define storage and loss moduli for nonlinear rheological materials using LAOS, Fourier transform, and stress decomposition methods, providing a unified framework and practical evaluation example.

## Contribution

It establishes a unified conceptual scheme for defining generalized moduli in nonlinear rheology based on LAOS data and Lissajous plots.

## Key findings

- Established the relation between FT and SD approaches in LAOS.
- Provided a unified scheme for defining generalized moduli.
- Demonstrated evaluation of moduli from LAOS flow.

## Abstract

A large amplitude oscillatory shear (LAOS) is considered in the strain-controlled regime, and the interrelation between the Fourier transform (FT) and the stress decomposition (SD) approaches is established. Several definitions of the generalized storage and loss moduli are examined in a unified conceptual scheme based on the Lissajous--Bowditch plots. An illustrative example of evaluating the generalized moduli from a LAOS flow is given.