Influence of nonlocal and surface effects on nonlinear responses of nano-systems and nano-networks

• Published in: International journal of computational methods in engineering science and mechanics Vol. 26; no. 5; pp. 315 - 329
• Main Authors: Nguyen, Thai-Binh, Henprasert, Korrawee, Sopittanon, Thanyakorn, Tran, Minh Thi, Rungamornrat, Jaroon, Luong, Van Hai
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03.09.2025
• Subjects: co-rotational technique; Eringen model; Gurtin-Murdoch model; nano-networks; Nano-systems; nonlocal effect; surface stresses
• ISSN: 1550-2287; 1550-2295
• DOI: 10.1080/15502287.2025.2513277

This study introduces an efficient methodology for the nonlinear analysis of skeletal nano-systems and nano-networks. The approach employs a rigorous mathematical framework based on an enhanced Euler-Bernoulli beam theory, incorporating Gurtin-Murdoch surface elasticity and Eringen's nonlocal elasticity theories to model nano-scale effects and size-dependent behaviors. A nonlinear co-rotational formulation is utilized to derive the global force-displacement relationship and the global tangent stiffness matrix for nano-elements experiencing large displacements and rotations. Within the co-rotational system, the force-displacement relationship assumes small rotations, with automatic mesh refinement ensuring this assumption's validity by controlling the maximum relative rotation of each element. A standard assembly procedure is applied to construct the global tangent stiffness matrix and residual load vector for the system. The nonlinear algebraic equations are solved using the Newton-Raphson iterative method, complemented by an arc-length control strategy to handle large structural deformations. Once nodal degrees of freedom are determined, quantities such as internal forces, reactions, and displacements are obtained through post-processing. This fully validated technique is then used to explore the impact of surface and nonlocal effects on buckling, post-buckling, and bending responses in nano-systems and nano-networks. Results from detailed parametric studies reveal that these effects profoundly influence system stiffness and introduce pronounced size-dependent behavior, particularly when the characteristic length of the nano-system approaches the intrinsic material length scale.