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Growth-induced instabilities for transversely isotropic hyperelastic materials

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Abstract

This work focuses on planar growth-induced instabilities in three-dimensional bilayer structures, i.e., thick stiff film on a compliant substrate or a confined tissue. Growth-induced instabilities are examined in three-dimension for a different range of fiber stiffness with a five-field Hu-Washizu type mixed variational formulation as the first time in the literature to our best knowledge. The quasi-incompressible and quasi-inextensible limits of transversely isotropic materials were considered. A numerical example was solved by implementing the T2P0F0 element on an automated differential equation solver platform, FEniCS. There was proposed a 2D modelling procedure based on a long but thin bilayer plate for the determination of exact wavelengths which plays key role in the periodic boundary condition in 3D plate. It was shown that both the wavelength and critical growth parameter g decrease by increasing the fiber stiffness for the first instability, which is obtained along the stiff fiber direction. The effect of the fiber stiffness is minor on the secondary buckling, which was observed perpendicular to the fiber direction. For a range of fiber stiffnesses, bifurcation points of instabilities were also determined by monitoring displacements and energies. The energy contributions of layers with different ranges of fiber stiffnesses were examined. It is concluded that the energy release mechanism at the initiation of the primary buckling is mainly due to isotropic and anisotropic contributions of the stiff film layer. For high fiber stiffnesses, the effect of the anisotropic energy on the first buckling becomes more dominant over other types. However, in the secondary instability, the isotropic energy of the film layer becomes the dominant one. Numerical outcomes of this study will help to understand the fiber stiffness effect on the buckling and post-buckling behavior of bilayer systems and fiber-reinforced soft biological tissues.

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  1. Department of Mechanical Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, Ankara, 06800, Turkey

    Cem Altun & Hüsnü Dal

  2. Department of Aerospace Engineering, Middle East Technical University, Dumlupınar Bulvarı 1, Ankara, 06800, Turkey

    Ercan Gürses

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  1. Cem Altun
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Altun, C., Gürses, E. & Dal, H. Growth-induced instabilities for transversely isotropic hyperelastic materials. Mech Soft Mater 5, 7 (2023). https://doi.org/10.1007/s42558-023-00055-8

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