A thermodynamically consistent strain-gradient model for functionally graded nanobeams with composite damage mechanics on elastic substrate medium
This theoretical study develops a thermodynamically consistent strain-gradient model for functionally graded Euler-Bernoulli nanobeams on a Winkler foundation. Damage is assigned to the ceramic phase while the metal remains intact. Voigt, Reuss and a proposed effective-property formulation are compared in analytical static-bending solutions. Damage lowers stiffness and increases deflection, while greater ceramic content and foundation stiffness increase rigidity; the proposed response remains between the Voigt and Reuss bounds.