Physics-informed neural network-based homogenization for architected lattice structures

Abstract

Pronounced size-dependent mechanical behavior is experimentally observed in architected lattice structures when the lattice constant varies, even under identical microstructural configurations. Conventional homogenization approaches, however, fail to capture this configuration-dependent size effect. To address this limitation, a physics-informed neural network (PINN)-based homogenization is proposed to homogenize architected lattice structures and solve the governing equations derived from the nonlocal strain gradient homogenization model (NSGHM) that incorporates high-order nonlocal integral terms. Two-phase NSGHM introducing dimensional nonlocal length and strain gradient length can characterize size effects arising from nonlocal interactions and strain gradient contributions. The PINN-based solver efficiently resolves the integro-differential equations derived from the NSGHM, overcoming computational bottlenecks inherent to nonclassical mechanics. The resulting PINN-based NSGHM framework accurately and efficiently predicts size-dependent mechanical responses of various lattice structures and demonstrates strong agreement with high-fidelity finite element simulations. This framework enables efficient and accurate multiscale modeling of architected materials, providing deeper insight into the configuration-driven size effects in lattice structures.