In a recent study, Kumar and Lopez-Pamies (J. Mech. Phys. Solids 150: 104359, 2021) have provided a complete quantitative explanation of the famed poker-chip experiments of Gent and Lindley (Proc. R. Soc. Lond. Ser. A 249: 195--205, 1959) on natural rubber. In a nutshell, making use of the fracture theory of Kumar, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 112: 523--551, 2018), they have shown that the nucleation of cracks in poker-chip experiments in natural rubber is governed by the strength -- in particular, the hydrostatic strength -- of the rubber, while the propagation of the nucleated cracks is governed by the Griffith competition between the bulk elastic energy of the rubber and its intrinsic fracture energy. The main objective of this paper is to extend the theoretical study of the poker-chip experiment by Kumar and Lopez-Pamies to synthetic elastomers that, as opposed to natural rubber: ($i$) may feature a hydrostatic strength that is larger than their uniaxial and biaxial tensile strengths and ($ii$) do not exhibit strain-induced crystallization. A parametric study, together with direct comparisons with recent poker-chip experiments on a silicone elastomer, show that these two different material characteristics have a profound impact on where and when cracks nucleate, as well as on where and when they propagate. In conjunction with the results put forth earlier for natural rubber, the results presented in this paper provide a complete description and explanation of the poker-chip experiments of elastomers at large. As a second objective, this paper also introduces a new fully explicit constitutive prescription for the driving force that describes the material strength in the fracture theory of Kumar, Francfort, and Lopez-Pamies.

翻译：在近期研究中，Kumar与Lopez-Pamies（J. Mech. Phys. Solids 150: 104359, 2021）对Gent和Lindley（Proc. R. Soc. Lond. Ser. A 249: 195–205, 1959）关于天然橡胶的著名扑克牌实验给出了完整的定量解释。简言之，他们基于Kumar、Francfort和Lopez-Pamies（J. Mech. Phys. Solids 112: 523–551, 2018）的断裂理论，证明了天然橡胶扑克牌实验中裂纹的成核由橡胶的强度（特别是静水强度）主导，而裂纹扩展则受橡胶的弹性体能量与固有断裂能量之间的Griffith竞争机制控制。本文主要目的是将Kumar与Lopez-Pamies对扑克牌实验的理论研究拓展至合成弹性体——与天然橡胶不同，这类材料（i）可能表现出大于单轴和双轴拉伸强度的静水强度，且（ii）不呈现应变诱导结晶。参数化研究及与近期硅酮弹性体扑克牌实验的直接对比表明，这两种材料特性差异对裂纹成核的位置与时机，以及扩展的位置与时机具有深远影响。结合先前关于天然橡胶的研究成果，本文研究结果为各类弹性体的扑克牌实验提供了完整的描述与解释。作为第二个目标，本文还针对Kumar、Francfort和Lopez-Pamies断裂理论中描述材料强度的驱动力，提出了一种全新的显式本构模型。