Determination of characteristic lengths of fcc metals within anisotropic second strain molecular simulations

V Bagherpour and MR Delfani, EUROPEAN JOURNAL OF MECHANICS A-SOLIDS, 107, 105377 (2024).

DOI: 10.1016/j.euromechsol.2024.105377

In this paper, a mathematical formalism of an anisotropic second strain gradient theory for describing the elasticity of hexoctahedral centrosymmetric cubic crystals is developed. It is shown that the equilibrium equations for a material belonging to the mentioned class of crystals within this theory include sixteen characteristic lengths. Although the number of these characteristic lengths is indeed large, there is no way accurately capture the elastic behavior of such crystals within the adopted theory unless the numerical values of all their characteristic lengths are to be available. Hence, a computational method for the determination of these characteristic lengths is proposed in the present paper. Molecular simulations of a few face -centered cubic (fcc) metals, which belong to the mentioned class of cubic crystals, subjected to appropriate modes of deformation are performed, and the corresponding analytical expressions are then fit to the data points obtained by these simulations. As a result of this procedure, all sixteen characteristic lengths of the fcc metals under consideration are determined. Moreover, an equivalent isotropic elastic medium within Mindlin's second strain gradient theory is introduced for fcc metals, and using a Voigt-type averaging method, the effective characteristic lengths of such an equivalent isotropic medium are then determined.

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