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As revealed by longitudinal bar resonance experiments, materials such as rocks and concrete show a rich diversity of nonlinear elastic behavior. As a function of increasing drive level, resonance frequencies shift downward by several percent, the resonant line shape changes, and harmonics and slow dynamics appear. Slow dynamics  refers to the timedependent recovery of an elastic modulus to its initial value after being softened by large strain. In order to explore the mechanisms of nonlineardoi:10.1063/1.1309228 fatcat:2vzcciqq6zaj5ceejmgblazbiy