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Peridynamic theory has been shown to possess the capabilities of describing phenomena that theories based on partial differential equations are not capable of describing. These phenomena include nonlocal interactions and presence of singularities in system responses. To exploit the capabilities offered by peridynamics in the homogenization of heterogenous media, a nonlocal computational homogenization theory based on peridynamic correspondence model (non-ordinary state-based peridynamics) is proposed. To set the development of the theory on a rigorous mathematical framework and to ensure consistency with the nonlocal nature of the peridynamic theory, a nonlocal vector calculus was used in the analysis of the nonlocal homogenization theory. The proposed theory is a two-scale micro–macro-homogenization strategy in which the constitutive relation at the macroscale is derived from explicit solution of a nonlocal volume constraint problem at the microscale. To justify the coupling between the two scales, nonlocal analogues of the stress and strain average theorems as well as the Hill–Mandel macrohomogeneity condition were derived. Validation of the proposed theory is achieved via numerical solution of Representative Volume Elements (RVE) from composite materials and comparing the results with those obtained by means of established methodologies.

In this study, free vibration analysis of cracked plates was performed by using peridynamics. Peridynamics is a new continuum mechanics formulation which is especially suitable for problems including discontinuities such as cracks. A peridynamic Mindlin plate formulation was used and the numerical implementation was done using commercial finite element software, ANSYS. First, the formulation was verified by considering intact and cracked plates and peridynamic solutions were compared against numerical, theoretical and experimental results available in the literature. Once the formulation was verified, the effect of plate thickness, crack size and crack orientation on the natural frequencies were investigated for a centrally cracked plate. It was found that natural frequency values increase as plate thickness increases. On the other hand, increase in crack length decreases the natural frequency values. Moreover, crack orientation also increases natural frequencies for larger cracks. Finally, linear variation of thickness inside the plate causes a tilt of the mode shapes towards the thin side of the plate.

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In this study, buckling analysis of cracked plates is performed by using peridynamics. A peridynamic Mindlin plate formulation is used and the numerical implementation is done using commercial finite element software, ANSYS. Critical buckling load is obtained by utilizing ANSYS Eigenvalue Buckling Analysis feature. Peridynamic results are compared against numerical and experimental results and a good agreement is obtained between different approaches. After verifying the formulation, it is utilised to investigate the effect of crack length, crack orientation and plate thickness on the critical buckling load values for a centrally and side-edge cracked plates subjected to clamped-free-clamped-free (CFCF) boundary conditions. Moreover, the effect of variable thickness on the critical buckling load is also examined.