Inverse Analysis of Cellulose by Using the Energy-Based Method and a Rotational Rheometer

Abstract

Biological and polymer-type materials usually show a complicated deformation behavior. This behavior can be modeled by using a nonlinear material equation; however, the determination of coefficients in such a material equation is challenging. We exploit representation theorems in continuum mechanics and construct nonlinear material equations for cellulose in an oscillatory rheometer experiment. The material parameters are obtained by using the energy-based method that generates a linear regression fit even in the case of a highly nonlinear material equation. This method allows us to test different nonlinear material equations and choose the simplest material model capable of representing the nonlinear response over a broad range of frequencies and amplitudes. We present the strategy, determine the parameters for cellulose, discuss the complicated stress-strain response and make the algorithm publicly available to encourage its further use.