Nonlinear softening of unconsolidated granular materials

Unconsolidated granular materials exhibit softening behavior due to external perturbations such as acoustic waves; namely, the wave speed and elastic modulus decrease upon increasing the strain amplitude. Recovery of the elastic modulus after the cessation of acoustic wave disturbance is logarithmic with time, over a span of hours or even years. I describe a theoretical model for such behavior. The model is based on the idea that shear transformation zones (STZs) -- clusters of grains that are loose and susceptible to contact changes, rearrangement and nonaffine displacement -- are responsible for plastic strain and softening of the material. We apply the theory to experiments on glass bead packs, and demonstrate that the theory predicts nonlinear resonance shifts and reduction of the P-wave modulus, in agreement with experiments. The theory thus offers insights on the implications of structural heterogeneities for damage, and failure in materials.