A Moment-of-Inertia-Dependent Surface Homogenization Method for Porous Polymer Beams

Obvious size-dependent bending responses are observed in porous polymer beams, particularly as their thickness approaches the scale of the lattice constant. However, the relationship between the size dependency and the microstructure remains unclear. Direct numerical simulations are computationally expensive due to the complexity of the microstructures, while classical multiscale methods, which neglect the surface effect, yield results that deviate significantly from actual behavior. In this study, an equivalent model for porous polymer beams incorporating surface-driven moment of inertia is developed to capture the size-dependent Young's modulus by introducing a surface strength factor and surface thickness. Then, an online prediction framework based on the offline dataset generated by the moment-of-inertia-dependent surface homogenization method was established for size-dependent bending response. The proposed framework is evaluated in terms of accuracy and computational efficiency. Results show that the classical multiscale homogenization method can produce relative errors as high as 1108%, whereas the surface homogenization method maintains relative errors below 4%. Moreover, the computational cost is substantially reduced compared to direct numerical simulations. This work not only uncovers the underlying moment-of-inertia-dependent surface mechanism of the size-dependent behavior in metamaterial beams but also delivers an accurate and efficient tool for their structural design and performance prediction.