Liu Zezhou, Jagota Anand, Hui Chung-Yuen
Department of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, 322 Kimball Hall, Ithaca, NY 14853, USA.
Departments of Bioengineering and of Chemical & Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA.
Soft Matter. 2020 Jul 29;16(29):6875-6889. doi: 10.1039/d0sm00556h.
Surfaces of soft solids can have significant surface stress, extensional modulus and bending stiffness. Previous theoretical studies have usually examined cases in which both the surface stress and bending stiffness are constant, assuming small deformation. In this work we consider a general formulation in which the surface can support large deformation and carry both surface stresses and surface bending moments. We demonstrate that the large deformation theory can be reduced to the classical linear theory (Shuttleworth equation). We obtain exact solutions for problems of an inflated cylindrical shell and bending of a plate with a finite thickness. Our analysis illustrates the different manners in which surface stiffening and surface bending stabilize these structures. We discuss how the complex surface constitutive behaviors affect the stress field of the bulk. Our calculation provides insights into effects of strain-dependent surface stress and surface bending in the large deformation regime, and can be used as a model to implement surface finite elements to study large deformation of complex structures.
软固体表面可能具有显著的表面应力、拉伸模量和弯曲刚度。以往的理论研究通常考察表面应力和弯曲刚度均为常数的情况，并假定变形较小。在本研究中，我们考虑一种通用公式，其中表面能够承受大变形，并同时承受表面应力和表面弯矩。我们证明了大变形理论可以简化为经典线性理论（Shuttleworth方程）。我们得到了充气圆柱壳问题和有限厚度板弯曲问题的精确解。我们的分析阐明了表面硬化和表面弯曲稳定这些结构的不同方式。我们讨论了复杂的表面本构行为如何影响体相的应力场。我们的计算为大变形状态下应变相关表面应力和表面弯曲的影响提供了见解，并且可以用作实现表面有限元以研究复杂结构大变形的模型。
