Physically admissible rules of evolution for discrete representations of continuous media

We propose a weighted residual procedure for defining physically admissible evolution rules for discrete models of generally anisotropic continuous media. The procedure is used to define 2D isotropic square Lattice Spring Models (LSM) of the Laplace, Maxwell, and Cauchy–Poisson equations. The latter LSM is employed to simulate the power law acoustic emission accompanying the microfracturing phenomenon in heterogeneous solids. We demonstrate the necessity and the advantages of physically admissible evolution rules, in comparison with commonly employed, ad hoc defined and empirically adjusted evolution rules.