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Abstract：
Wrinkling is a ubiquitous surface phenomenon in many biological tissues and is believed to play an important role in arterial health. As arteries are highly nonlinear, anisotropic, multilayered composite systems, it is necessary to investigate wrinkling incorporating these material characteristics. Several studies have examined surface wrinkling mechanisms with nonlinear isotropic material relationships. Nevertheless, wrinkling associated with anisotropic constitutive models such as Ogden-Gasser-Holzapfel (OGH), which is suitable for soft biological tissues, and in particular arteries, still requires investigation. Here, the effects of OGH parameters such as fibers\' orientation, stiffness, and dispersion on the onset of wrinkling, wrinkle wavelength and amplitude are elucidated through analysis of a bilayer system composed of a thin, stiff neo-Hookean membrane and a soft OGH substrate subjected to compression. Critical contractile strain at which wrinkles occur is predicted using both finite element analysis and analytical linear perturbation approach. Results suggest that besides stiffness mismatch, anisotropic features associated with fiber stiffness and distribution might be used in natural layered systems to adjust wrinkling and subsequent folding behaviors. Further analysis of a bilayer system with fibers in the (x-y) plane subjected to compression in the x direction shows a complex dependence of wrinkling strain and wavelength on fiber angle, stiffness, and dispersion. This behavior is captured by an approximation utilizing the linearized anisotropic properties derived from OGH model. Such understanding of wrinkling in this artery wall-like system will help identify the role of wrinkling mechanisms in biological artery in addition to the design of its synthetic counterparts.
摘要：
皱纹是许多生物组织中普遍存在的表面现象，被认为在动脉健康中起重要作用。由于动脉高度非线性，各向异性，多层复合体系,有必要研究结合这些材料特性的起皱。一些研究已经检查了具有非线性各向同性材料关系的表面起皱机制。然而，与各向异性本构模型相关的起皱，如Ogden-Gasser-Holzapfel(OGH)，适用于软生物组织，特别是动脉，仍然需要调查。这里,OGH参数的影响，如纤维的取向，刚度,和皱纹开始时的分散，通过分析由薄层组成的双层系统来阐明皱纹的波长和振幅，坚硬的neo-Hookean膜和经受压缩的柔软OGH底物。使用有限元分析和分析线性扰动方法来预测出现皱纹的临界收缩应变。结果表明，除了刚度不匹配，与纤维刚度和分布相关的各向异性特征可用于自然分层系统以调节起皱和随后的折叠行为。对（x-y）平面中的纤维在x方向上受到压缩的双层系统的进一步分析显示，起皱应变和波长对纤维角度的复杂依赖性，刚度,和分散。通过利用从OGH模型导出的线性化各向异性特性的近似来捕获这种行为。这种对这种动脉壁样系统中起皱的理解将有助于确定起皱机制在生物动脉中的作用，以及其合成对应物的设计。
