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Article Citation - WoS: 5Citation - Scopus: 5Physics-Informed Neural Network for Bending Analysis of Twodimensional Functionally Graded Nano-Beams Based on Nonlocal Strain Gradient Theory(Univ Tehran, Danishgah-i Tihran, 2025) Esfahani, Saba Sadat Mirsadeghi; Fallah, Ali; Aghdam, Mohammad MohamadiThis paper presents the bending analysis of two-dimensionally functionally graded (2D FG) nano-beams using a physics-informed neural network (PINN) approach. The material properties of the nanobeams vary along their length and thickness directions, governed by a power-law function. Hamilton's principle, combined with the nonlocal strain gradient theory (NSGT) and Euler-Bernoulli beam theory, is employed to derive the governing equation for the bending analysis of 2D FG nanobeams. Due to the incorporation of size dependency and the variation of material properties in two dimensions, the governing equation becomes a high-order variable- coefficient differential equation, which is challenging, if not impossible, to solve analytically. In this study, the applicability of PINN for solving such high-order complex differential equations is investigated, with potential applications in nanomechanical engineering. In the PINN approach, a deep feedforward neural network is utilized to predict the mechanical response of the beam. Spatial coordinates serve as inputs, and a loss function is formulated based on the governing equation and boundary conditions of the problem. This loss function is minimized through the training process of the neural network. The accuracy of the PINN results is validated by comparing them with available reference solutions. Additionally, the effects of material distribution, power-law index (in both length and thickness directions), nonlocal strain gradient parameters, and material length scale parameters are investigated. This study demonstrates the versatility of the PINN approach as a robust tool for solving high-order differential equations in structural mechanics.Article Citation - WoS: 2Citation - Scopus: 2Large Deflection Analysis of Functionally Graded Reinforced Sandwich Beams With Auxetic Core Using Physics-Informed Neural Network(Taylor & Francis inc, 2025) Nopour, Reza; Fallah, Ali; Aghdam, Mohammad MohammadiThis paper aims to investigate the large deflection behavior of a sandwich beam reinforced with functionally graded (FG) graphene platelets (GPL) together with an auxetic core, rested on a nonlinear elastic foundation. The nonlinear governing equations of the problem are derived using Hamilton's principle based on the Euler-Bernoulli beam theory for large deflections. Five different distributions are considered to describe the dispersion of GPL in the top and bottom faces of the sandwich beam. The Physics-Informed Neural Network (PINN) method is employed to model the nonlinear deflection of the beam under various boundary conditions. This study highlights the effectiveness of PINN in handling the complexities of nonlinear structural analyses. The findings underscore the impact of the core auxeticity, GPL amount and distribution, and elastic foundation coefficient on the nonlinear deflection of the sandwich beam under different loading scenarios. For instance, using Type I configuration can reduce the deflection of the beam by nearly half compared to using Type IV. Furthermore, a nonlinear foundation with a unit coefficient results in a 48% reduction in deflection compared to the scenario without an elastic foundation.Article Citation - WoS: 3Citation - Scopus: 34D Printing of Reusable Mechanical Metamaterial Energy Absorber, Experimental and Numerical Investigation(Iop Publishing Ltd, 2025) Fallah, Ali; Saleem, Qandeel; Scalet, Giulia; Koc, BahattinThis study investigates the compression behavior, energy absorption, shape memory properties, and reusability of 4D-printed smart mechanical metamaterials. Four structural configurations, i.e. honeycomb, re-entrant, and two modified re-entrant designs were developed to assess microstructure effects. Samples were fabricated using Polylactic Acid (PLA), a widely used shape memory polymer (SMP) in 4D printing, and polyethylene terephthalate glycol (PETG), an emerging SMP with demonstrated shape memory performance in recent studies. Cold-programming-induced shape recovery was evaluated at room temperature, simulating real-world conditions. Finite element simulations of compression and shape memory cycles matched experimental results well. Auxetic samples with negative Poisson's ratios showed superior energy absorption. However, only PETG demonstrated sufficient reusability, while PLA proved unsuitable for reusable designs. The PETG-3 modified re-entrant structure exhibited the best performance, with high energy absorption, delayed densification onset, and shape recovery and reusability factors of 0.95 and 0.96, respectively. Findings highlight the importance of considering both shape recovery and reusability when designing smart structures to address industrial challenges.