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.
Key findings
- Ceramic-phase damage reduced stiffness and increased deflection. • More ceramic content and a stiffer foundation increased rigidity. • The proposed formulation remained within Voigt-Reuss bounds.
Why this matters globally
The framework supports physically bounded analysis of damaged multi-material nanostructures, but still requires numerical and experimental validation.
Thai researcher contribution
Researchers from six Thai universities collaborate on nanoscale structural mechanics and damage modeling.
Limitations to consider
The static Euler-Bernoulli/Winkler assumptions omit shear, dynamics, other nonlocal effects, complex damage evolution and material-level validation.