Simulation of deformation of lattices: point-to-point analysis and applications

When applied to homogeneous rocks, the statistical technique of autocorrelation helps in visualizing the preferential alignment of mineral barycenters. We examine the behaviour of each element within a regular lattice deformed in either simple or pure shear. Preferential directions immediately appear depending upon the relative orientation of the shear or flattening plane with respect to the lattice. Autocorrelation amplifies these directions (either one direction with a high intensity signal or two directions with weak intensity signals). They depend on the geometrical shape of the elementary mesh of the lattice which is changing during the deformation. From the autocorrelated diagram, geometrical parameters of the elementary mesh can be estimated. Resulting from the numerical simulations, graphs are constructed which provide strain estimates in the case of simple shear. Application to natural rocks deformation is given in the case of simple-sheared peridotites.