Dynamic fracture analysis of functionally graded viscoelastic anisotropic nanostructures with a blunt crack under transient Thermal-Mechanical loading

This study introduces an advanced size-dependent boundary element method (BEM) specifically developed for dynamic fracture analysis of functionally graded viscoelastic anisotropic nanostructures with a single blunt crack under transient thermal–mechanical loading. The new formulation captures both fractional viscoelastic constitutive behavior and surface elasticity effects via the Gurtin–Murdoch model to capture more effectively nano-scale responses. A time-domain integral approach is developed with appropriate fundamental solutions for anisotropic solids such that stress intensity factors (SIF), crack opening displacements (COD), and stress concentration factors (SCF) can be precisely determined under dynamic loading conditions. The method requires discretization on boundaries only, lowering computational cost significantly but with very high resolution available at crack tips and stress singularities. Extensive validation against finite element and analytical solutions demonstrates excellent agreement with relative errors of less than 2%. Parametric analyses demonstrate the significant influence of fractional order, surface elasticity, and material grading on the evolution of dynamic fracture parameters. The results confirm that the proposed BEM method is not only numerically efficient but also physically accurate for fracture predictive analysis in micro- and nano-device structures, e.g., MEMS/NEMS, subjected to coupled field and time-dependent loading conditions.