Nonlinear resonance measurements provide the means to make very precise determination of material properties (e.g., modulus) as well as to ascertain damage. Nonlinear resonance measurements made on concrete cores show many similarities to measurements made on earth materials. Resonance peak shifts and memory effects can both be used to ascertain damage. For example, for (modulus) recovery of a sample to moderate strain (106) has been found to be initially logarithmic in time and has been measured to 1 ppm with a very simple apparatus under less than ideal conditions. Moreover, the modulus softening observed as excitation level is increased is related to the amount of cracking and damage that exists within a sample. The magnitude of nonlinearity (measured by finding the peak shifts as a function of drive amplitude) is found, in concrete samples, to correlates strongly with ASR damage. These results suggest a viable method to determine the extent of cracking. The scaling of the nonlinear peak shift with str...