Viscoelastic properties of plant cell walls. IV. Physical meaning of parameter K in mathematical formulation for stress-relaxation and load-extension processes

Abstract

When the function ϕ(K, A; B) is defined by the equation $$\begin{array}{c}\mathit{\varphi }\mathrm{(}\mathrm{K}\mathrm{,}\mathrm{A};\mathrm{B}\mathrm{)}=\mathrm{B}{\mathrm{(}1+{\displaystyle \frac{\mathrm{A}}{\mathrm{B}}}\mathrm{)}}^{1+\frac{\mathrm{B}-\mathrm{K}}{\mathrm{A}}}\end{array}$$ the stress-relaxation process at a fixed strain has been represented in the previous papers of this series as follows: $$\begin{array}{c}\mathrm{S}={\mathrm{b}}_{\mathrm{k}}·ln{\displaystyle \frac{\mathit{\varphi }\mathrm{(}\mathrm{K}\mathrm{,}{\mathrm{t}}_{\mathrm{p}};\mathrm{t}+{\mathrm{T}}_{\mathrm{mk}}\mathrm{)}}{\mathit{\varphi }\mathrm{(}\mathrm{K}\mathrm{,}{\mathrm{t}}_{\mathrm{p}};\mathrm{t}+{\mathrm{T}}_{\mathrm{ok}}\mathrm{)}}}+{\mathrm{c}}_{\mathrm{k}}\end{array}$$ where S is stress, t_p is pre-extension time, and the parameters T_ok, T_mk, b_k, c_k, and K are constants. As we have reported, the parameters T_ok, T_mk, b_k, and c_k can be defined physically. However, the physical meaning of the parameter K has remained unclear. This study leads to the conclusion that parameter K can be defined as being equal to the pre-extension time, t_p, in the stress-relaxation experiment. Thus, the stress-relaxation curve and the effect of auxin pretreatment on a hysteresis loop in a stress-strain curve at a constant rate could be represented well by the calculated values.