Strain-stiffening behavior of materials such as rubberlike materials and biological soft tissues is an important phenomenon. In this paper, we proposed a surface Green’s function tensor to describe the strain-stiffening behavior of the stretchable elastomer based on the Gent constitutive model. The surface Green’s function tensor of the Gent constitutive model can be recovered to that of neo-Hookean model, and applied to the indentation problem with a flat-ended cylindrical indenter. The relation between the indentation force and strain-stiffening parameter is analytically derived for equi-biaxial prestretched elastomers. The study shows that the strain-stiffening of the elastomer has a great impact on indentation behaviors, especially for the cases of large prestretches. For a given indentation depth, the indentation force decreases with the increase of the strain-stiffening parameter. For a given stiffening parameter, the indentation force increases with the increase of the prestretches. The proposed surface Green’s function tensor has also potential applications in other fields, such as wetting, cell migration, self-assembly on strain-stiffening materials, etc.

中文翻译：

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预拉伸应变硬化弹性体的压痕

橡胶类材料和生物软组织等材料的应变硬化行为是一个重要现象。在本文中，我们基于 Gent 本构模型提出了一个表面格林函数张量来描述可拉伸弹性体的应变硬化行为。Gent本构模型的表面格林函数张量可以恢复到neo-Hookean模型的表面格林函数张量，并应用于带有平头圆柱压头的压痕问题。对于等双轴预拉伸弹性体，压痕力和应变硬化参数之间的关系是通过分析推导出来的。研究表明，弹性体的应变硬化对压痕行为有很大影响，特别是对于大预拉伸的情况。对于给定的压痕深度，压痕力随着应变硬化参数的增加而减小。对于给定的刚度参数，压痕力随着预拉伸的增加而增加。所提出的表面格林函数张量在其他领域也有潜在的应用，如润湿、细胞迁移、应变硬化材料的自组装等。