This study investigates the deformation-dependent nonlinear forced vibration behavior of a nanocomposite hyperelastic beam reinforced with MXene nanoparticles, where both geometric and material nonlinearities are fully considered through a higher-order beam formulation. The hyperelastic behavior of the PDMS matrix is modeled using the modified Neo-Hookean constitutive model, while MXene reinforcement is incorporated via the Halpin–Tsai homogenization approach. The governing equations are derived using Hamilton’s principle and discretized through the Galerkin method. A dual numerical strategy is employed: the fourth-order Runge–Kutta method for transient time-history analysis, and a physics-driven gradient learning framework combined with Fourier series expansion for steady-state frequency response extraction. Key findings reveal that increasing the MXene volume fraction to 15% and 30% reduces the static deflection by 15.20% and 27.02%, respectively, due to enhanced effective stiffness. The frequency response exhibits pronounced hardening-type nonlinearity with multivalued branches and jump phenomena, which are significantly influenced by the dynamic pressure level. Comparative analysis shows that material nonlinearity reduces the vibration amplitude by 7.46% compared to considering only geometric nonlinearity. The proposed model provides a reliable framework for designing lightweight, multifunctional soft structures operating under large dynamic deformations.
The numerical prediction of delamination events in engineering structures has attracted considerable research attention in the last three decades. Within this context, cohesive zone models (CZMs) have emerged as widely adopted computational tools for this purpose. However, CZMs usually suffer from notable mesh requirements for achieving converged equilibrium solutions, arising from the inherent nonlinear relationship between the traction vector and the displacement gap along the interface. Practical guidelines suggest the use of between 2–5 elements within the so-called fracture process zone (FPZ) in order to alleviate such convergence issues, and alternatively the modification of the interface strength properties via enlarging the FPZ in the corresponding model. In an effort to address these limitations, we propose a strength-reduction cohesive interface model in which the reduction factor is linked to a fracture process zone length that adapts locally to the mode mixity through the Benzeggagh–Kenane parameter, rather than being prescribed a priori as in existing strength-reduction approaches. An auxiliary nonlocal damage field, governed by a Helmholtz-type partial differential equation, is additionally introduced to provide a mesh-objective, spatially regularised representation of the damage distribution; in the present formulation this field does not feed back into the traction–separation law, and its two-way coupling with the constitutive response is identified as a natural extension. This model is implemented in the FE software ABAQUS as a user-defined element. Several representative examples assess the performance of the developed model under different fracture mode conditions, showing the efficiency of the proposed strength-reduction mechanism and its adaptivity to evolving mode mixity.
