Interaction of two nearby CNTs/nanovoids embedded in a metal matrix using modified nonlocal elasticity

Interaction of Carbon Nanotubes (CNTs) and nanovoids embedded in a metal matrix is studied comparatively. For this purpose, two nearby CNTs/nanovoids are modeled as two similar cylindrical inclusions/holes in an infinite matrix. The nonlocal stresses around the CNTs/nanovoids are obtained by applying the integral constitutive equation of the nonlocal elasticity to the stresses from the complex stress potential method. Also, in order to bring different nonlocality effects of dissimilar media into account, the influence function of the nonlocal elasticity is modified. Effects of the CNTs/nanovoids size and distance as well as far-field loading ratio on the stress state in the matrix are investigated. The CNTs strengthening effect on the matrix is shown through lower stresses at the CNTs and matrix interface in comparison to the applied stress. Furthermore, it is indicated that the modified nonlocal analysis brings out the interaction of CNTs/nanovoids at smaller distances in comparison with those the classical analysis used to predict. In other words, higher volume fraction of the CNTs/nanovoids can be incorporated in the metal matrices without devastating effects of their interactions.