Formulation of Pre-Extension in a Practical Stress-Relaxation Measurement of the Plant Cell Wall

Abstract

In practical measurement of stress-relaxation, a certain length of time is required to apply the initial stress to a specimen. We refer to this process as pre-extension. In the stress-relaxation analysis of the plant cell wall which we developed, a wall specimen is stretched at a constant rate in pre-extension. The condition of pre-extension, such as the length of the pre-extension period, affects the subsequent stress-relaxation process. Thus, the stress-relaxation time spectrum calculated directly from the stress-relaxation process is an approximation. In this study, the condition during pre-extension was formulated in a stress-relaxation function and the stress-relaxation time spectrum, $\mathit{H}\mathrm{(}\mathit{\tau }\mathrm{)}$ , was calculated as $$\begin{array}{c}\mathit{H}\mathrm{(}\mathit{\tau }\mathrm{)}=\mathit{b}·\{exp\mathrm{(}-{\mathit{T}}_0\mathrm{/}\mathit{\tau }\mathrm{)}-exp\mathrm{(}-{\mathit{T}}_{\mathit{m}}\mathrm{/}\mathit{\tau }\mathrm{)}\}\mathrm{/}\{\mathit{r}·\mathit{\tau }·\mathrm{(}\mathit{l}-exp\mathrm{(}-{\mathit{T}}_{\mathit{p}}\mathrm{/}\mathit{\tau }\mathrm{)}\mathrm{)}\}\end{array}$$ where ${\mathit{T}}_0$ and ${\mathit{T}}_{\mathit{m}}$ are the minimum and maximum relaxation times, τ is the relaxation time, b is the relaxation rate, r is the extension rate in pre-extension and ${\mathit{T}}_{\mathit{p}}$ is the pre-extension time. The effect of the pre-extension condition on the spectrum is discussed.