Microfibrillar buckling within fibers under compression

A tentative theory is presented of microfibrillar buckling within compressed fibers. A quantitative harmonic analysis is given of the semiclassical buckling of a clamped stiff chain; the influence of thermal undulations is incorporated in Euler buckling. A scaling analysis including entropy allows one to understand semiclassical buckling. The buckling of a microfibril within a fibrous environment is analyzed in two limits: (a) when the fiber is incompressible; (b) when the matrix is assumed to be a fixed harmonic potential. In the latter case, a network of microfibrils may melt at high enough compression before the usual buckling occurs. We also study the renormalization of the confining potential by long-range elastic fields. A provisional comparison with experimental studies on macroscopic failure is given.