Identification method of gradient models parameters of inhomogeneous structures based on discrete atomistic simulations

This paper considers characteristics, features and corresponding boundary value problems of gradient theories of elasticity. A brief description of one-parametric applied model, which is one of the several variants of the gradient elasticity theories is given here. In relation to that, we represent a con- tinuum gradient model of two-phase composite structures that allow evaluation of the influence of scale parameters on their effective mechanical properties.In identifying the additional physical parameters of gradient elasticity models, a new method is introduced where a comparison of the results of continuum and discrete-atomistic modelling for specific tested heterogeneous structures is made. As a result we suggested a procedure and the respective algorithm defining the additional parameter of applied gradient continuum model of heterogeneous me- dia; and in such procedure, an interphase zone is characterized at the contact surface of a two-phase composite and the scale effects represented by cohesions-interaction fields, which are localized near to the boundaries of contact surfaces. This additional physical parameter of gradient model is found through parameters of potentials, which are used to describe the specific studied structure in the dis- crete-atomistic modelling.To justify and validate the proposed method, a numerical investigation is conducted and com- parison is made between the results of continuum and discrete-atomistic modelling. The examination reveals that a high degree of accuracy of prediction can be provided by the continuum one-parametric gradient theory when describing the effective properties of countable multiple set of two-phase hetero- geneous studied structures, which are formed by atomic substructures with various properties (various parameters of potentials).Finally, it is demonstrated that the identification method of parameters in gradient elasticity theo- ries for heterogeneous structures is well described by Leonard-John potential and Morse potential. Fur- thermore, we consider that when the parameters of potentials are known, the various types of cross interactions of atoms can be treated as ‘ideal’ or ‘damaged’ interactions as per Lorentz-Berthelot’s rule.