Bifurcation, localization, energy barriers and hysteresis in elastic structures and materials
John W. Hutchinson
School of Engineering and Applied Sciences, Harvard University *
Examples drawn from experiments and analysis of shell structures and soft material systems are used to illustrate a sequence of instability phenomena comprising localization of the bifurcation mode accompanied by loss of quasi-static stability with dynamic snapping to a large amplitude localized deflection. Under cyclic loading which pushes into the large amplitude regime in each cycle, hysteretic behavior occurs even when the material response is strictly elastic. The transition to the large amplitude deflection is characterized by an energy barrier which serves to measure the tolerance to both unexpected disturbances and deliberate probing of the structure or material. Recent theoretical and experimental efforts to exploit a force probe to assess the degree of stability of loaded structures will be discussed.