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In soft matter systems the local displacement field can be accessed directlyby video microscopy enabling one to compute local strain fields and hence theelastic moduli using a coarse-graining procedure. We study this process for asimple triangular lattice of particles connected by harmonic springs intwo-dimensions. Coarse-graining local strains obtained from particleconfigurations in a Monte Carlo simulation generates non-trivial, non-localstrain correlations (susceptibilities), which may be understood within ageneralized, Landau type elastic Hamiltonian containing up to quartic terms instrain gradients (K. Franzrahe et al., Phys. Rev. E 78, 026106 (2008)). Inorder to demonstrate the versatility of the analysis of these correlations andto make our calculations directly relevant for experiments on colloidal solids,we systematically study various parameters such as the choice of statisticalensemble, presence of external pressure and boundary conditions. We show thatspecial care needs to be taken for an accurate application of our results toactual experiments, where the analyzed area is embedded within a larger system,to which it is mechanically coupled. Apart from the smooth, affine strainfields, the coarse-graining procedure also gives rise to a noise field made upof non-affine displacements. Several properties of this noise field may berationalized for the harmonic solid using a simple "cell model" calculation.Furthermore the scaling behavior of the probability distribution of the noisefield is studied and a master curve is obtained.

physical review. e, statistical, nonlinear and soft matter physics

Coarse-graining microscopic strains in a harmonic, two-dimensional solid  and its implications for elasticity: non-local susceptibilities and  non-affine noise