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.
Highlights
In polymer science and biological tissue modeling, the material response fails to be modeled accurately by a linear material equation
We have presented the measurements and the energy-based method for determining the material constants of a nonlinear material equation
The nonlinear response of cellulose has been investigated by using standard oscillatory rheometer measurements
Summary
In polymer science and biological tissue modeling, the material response fails to be modeled accurately by a linear material equation. The material coefficient, called viscosity, is a constant, and since a constant fails to attain an accurate modeling, there are various approaches to increase the complexity by choosing a viscosity depending on the velocity gradient [1]. Instead of a material equation with a rate, integral equations were proposed in order to include the full history on deformation as in [10,11]. These equations were used as models in [12], and measurements were undertaken in [13]. As stated in [18], the nonlinear modeling in rheology is still an open question, and we cannot expect to acquire a consensus; but we need tools making the inverse
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