Abstract

Cracked orthotropic plates resting on viscoelastic foundations exhibit complex dynamic responses due to the simultaneous influence of nonlocal elasticity, memory-dependent damping, and displacement discontinuities. Conventional models often fail to capture these effects in a unified manner, particularly when fractional-order formulations are required. In this study, a fractional-order extended finite element method (XFEM) framework is developed for the dynamic analysis of orthotropic rectangular plates with internal cracks on fractional viscoelastic foundations. The methodology combines Caputo time-fractional derivatives to model inertia memory and hereditary damping with Riesz space-fractional derivatives to represent nonlocal stiffness. Crack discontinuities are incorporated using Heaviside functions for crack faces and asymptotic crack-tip enrichment functions within XFEM. The governing equations are transformed using Fourier and Laplace transforms, and closed-form analytical solutions are obtained by Fox H-function inversion, with explicit convergence conditions provided to ensure mathematical validity. Numerical simulations investigate the influence of crack length, fractional orders, and foundation stiffness on displacement profiles, energy dissipation, and dynamic stress intensity factors (DSIFs). Results show that lower time-fractional orders intensify memory effects and prolong oscillations, while higher spatial orders (alpha, B) and foundation shear order (delta) enhance stiffness and reduce peak displacements. Quantitative validation against benchmark solutions confirms the accuracy of the proposed formulation. The findings demonstrate that the integrated fractional XFEM approach provides a robust and generalizable framework for modeling cracked composite plates in aerospace, mechanical, and civil engineering applications, offering new insights into the multiscale interactions of cracks, nonlocal elasticity, and viscoelastic foundations.