MATHEMATICAL MODELING OF THE ELASTIC PROPERTIES OF COLLOIDAL CRYSTALS WITH ISOTROPIC INITIAL STRESS
The model assumptions are formulated to describe colloidal crystals with an isotropic initial stress. The approach to mathematical modeling of homogeneous deformation of the studied systems is considered. A method for determining the elastic constants of the first and second orders of colloidal crystals with an isotropic initial stress is proposed. The method is based on the determination of the numerical dependences of stress on deformation during a computational experiment. Based on the theory considered, an algorithm for determining the dependences of stress on strains as a function of crystal density is developed, model parameters are determined, and the design of a computational experiment is described. The proposed method can be used for computational experiments in a wide range of model parameters and is uniformly applicable to all three-dimensional and two-dimensional colloidal crystals with an isotropic initial stress, regardless of the type of lattice.