Magneto-Thermoelastic Fracture in Nonlocal Cracked Nanobeams using Modified Couple Stress Model with Memory Effect

The study of thermal characteristics in cracked nanobeams is vital for the reliable functioning of micro and nanoelectromechanical systems. Classical solid mechanics and Fourier heat law fail to accurately predict size-dependent elastic deformation and thermal hysteresis effects in such structures. To address this, a new computational model rooted in memory dependent derivatives is constructed to assess viscoelastic rotating cracked nanobeams subjected to a magnetic field and heat source. The model incorporates nonlocal generalized couple stress theory and generalized thermoelasticity considering memory dependent effects. The governing equations are derived based on the Euler-Bernoulli beam model, Maxwell's formulations, and a fractional-order Kelvin-Voigt viscoelastic framework. The deflection, temperature field, displacement, and bending moment of the cracked nanobeam are numerically determined using the Laplace transform and its inverse.