Analytical and Numerical Simulation of Hyperelastic Two-Phase Periodic Laminates

Analytical and Numerical Simulation of Hyperelastic Two-Phase Periodic Laminates

Aguiar, Adair R.; Prado, Edmar B. T.

Abstract:

Laminated composite structures are employed in a wide range of engineering applications and demand a proper understanding of their physical behavior. Usually, the associated problems to these applications are nonlinear and the corresponding solutions are not known. Analytical and numerical methods are used to search for approximate solutions to these problems, which may lose ellipticity at large enough deformations even though the materials of the laminae do not exhibit any stability issues. These solutions are used here to investigate the influence of the microstructure in the global behavior of the laminate. In particular, we study two-phase periodic laminates made of hyperelastic laminae and subjected to a pure shear state on their boundaries. Using the finite element method (FEM), the angle of lamination in the deformed configuration of the laminate is calculated and compared to the corresponding angle obtained via AHM. Both angles are very close to each other up to a critical shear deformation. At this deformation, the angle obtained via FEM changes abruptly from the angle obtained via AHM. As the deformation increases, the differences between the angles become constant and considerably large. Justification for this bifurcation-like behavior and a study of the influence of the bulk modulus on this behavior are also presented.

Laminated composite structures are employed in a wide range of engineering applications and demand a proper understanding of their physical behavior. Usually, the associated problems to these applications are nonlinear and the corresponding solutions are not known. Analytical and numerical methods are used to search for approximate solutions to these problems, which may lose ellipticity at large enough deformations even though the materials of the laminae do not exhibit any stability issues. These solutions are used here to investigate the influence of the microstructure in the global behavior of the laminate. In particular, we study two-phase periodic laminates made of hyperelastic laminae and subjected to a pure shear state on their boundaries. Using the finite element method (FEM), the angle of lamination in the deformed configuration of the laminate is calculated and compared to the corresponding angle obtained via AHM. Both angles are very close to each other up to a critical shear deformation. At this deformation, the angle obtained via FEM changes abruptly from the angle obtained via AHM. As the deformation increases, the differences between the angles become constant and considerably large. Justification for this bifurcation-like behavior and a study of the influence of the bulk modulus on this behavior are also presented.

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Como citar:

Aguiar, Adair R.; Prado, Edmar B. T.; "Analytical and Numerical Simulation of Hyperelastic Two-Phase Periodic Laminates", p-55-55. In: Proceedings of the 13th International Symposium on Multiscale, Multifunctional and Functionally Graded Materials [=Blucher Material Science Proceedings, v.1, n.1]. São Paulo: Blucher, 2014.
ISSN 23589337, DOI