Second-order phase transition and universality of self-buckled elastic slender columns

摘要

Self-buckling is an interesting phenomenon that is easily found around us, either in nature or inobjects made by human. Palm fronds which initially directed upward when they were short andturned into bending after appreciably longer is an example of the self-buckling phenomenon.We report here that the self-buckling of columns can be treated as a process of second-orderphase transition by considering the straight column as “disorder state”, the bending column as“order state”, and the temperature as the inverse of column length. The “critical temperature”corresponds to the inverse of critical length for buckling, 1/Lcr, and the deviation angle made bycolumn free end relative to vertical direction satisfies a scaling relationship with a scaling powerof 0.485. Changing of the column geometry from the vertically upward to the bending state canbe considered as a transition from disorder state to order state.