Nonlocal elastic compliance for soft solids: theory, simulations, and experiments.

The nonlocal elastic response function is crucial for understanding many properties of soft solids. This may be obtained by measuring strain-strain autocorrelation functions. We use computer simulations as well as video microscopy data of superparamagnetic colloids to obtain these correlations for two-dimensional triangular solids. Elastic constants and elastic correlation lengths are extracted by analyzing the correlation functions. We show that to explain our observations displacement fluctuations in a soft solid need to contain affine (strain) as well as nonaffine components.