Dynamic behavior of heterogeneous neo-Hookean/Mooney–Rivlin plates reinforced nonuniformly by hyperelastic inclusions: Proposing the correct micromechanical model

Abstract

Time-dependent nonlinear lateral vibrations of plates composed of a hyperelastic matrix and uniformly/nonuniformly distributed hyperelastic reinforcing inclusions are studied. Since the material constants of a hyperelastic must be extracted from the whole slope-varying stress-strain curve rather than a single slope, choosing power/exponential distributions for the material constants or using Voigt’s rule of mixtures is quite wrong. The neo-Hookean and Mooney–Rivlin constitutive models are adopted, and their results are compared. Another hint is incorporating the incompressibility condition. The governing equations of motion are derived by using Hamilton’s principle, a new energy-equivalence-based micromechanical model that can be employed for reinforcing phases with nonlinear constitutive laws, and von Kármán assumptions in the left Cauchy–Green deformation tensor, and solved by incorporation of an updating finite-element and Newmark’s techniques. Not only the displacement but typical stress results are also reported here. Results show that the neo-Hookean model overestimates the rigidity in comparison to the Mooney–Rivlin model, and unlike the elastic plates, the effect of the stiffer phase is more remarkable in the uniform distribution in comparison to the nonuniform distribution of the stiffening materials because the magnitudes of the tensile stresses of the hyperelastic plate are much larger than that of the bending stresses.

On the wave dispersion of a multi-scale hybrid nanocomposite microstructure via deep neural network technique

“…Therefore, artificial neural network (ANN) (Lingamdinne et al, 2023; Moradi et al, 2022) and PINN could be feasible procedures to obtain results in a short time span. The numerical solutions in structural mechanics have been used in nonlinear buckling (Al-Furjan et al, 2020a; Moayedi et al, 2020; Safarpour et al, 2020a, 2020b), wave propagation (Al-Furjan et al, 2021c; Ebrahimi et al, 2019b; Habibi et al, 2019b), and vibration (Sui et al, 2021; Dai et al, 2022) in different members including beams (Kharazan et al, 2021; Singh and Sharma, 2021; Ramírez-Neria et al, 2021; Shariati et al, 2020a, 2020b, 2020c), shells (Ansari et al, 2021; Habibi et al, 2019b, 2019c, 2021b), and plates (Shariyat and Khani Arani, 2022; Habibi et al, 2019a, 2021a; Huo et al, 2021). The nonlinear vibrations of shell structures with conical geometry made of composite materials and complicated cut-outs were investigated by Ansari et al (2021).…”

“…The subject of formulation in the solid mechanics for nonlinear behavior has been investigated for decades. Recently, a model was proposed by Shariyat and Khani Arani (Shariyat and Khani Arani, 2022) for examining dynamic modeling of heterogeneous plates with nonlinear hyperelastic behavior in micro-scale space.…”