当前位置: X-MOL 学术J. Mech. Phys. Solids › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Why does an elastomer layer confined between two rigid blocks grow numerous cavities?
Journal of the Mechanics and Physics of Solids ( IF 5.3 ) Pub Date : 2023-01-23 , DOI: 10.1016/j.jmps.2023.105223
Sida Hao, Zhigang Suo, Rui Huang

For a thin layer of elastomer sandwiched between two rigid blocks, when the blocks are pulled, numerous cavities grow in the elastomer like cracks. Why does the elastomer grow numerous small cracks instead of a single large crack? Here we answer this question by analyzing an idealized model, in which the elastomer is an incompressible neoHookean material and contains a penny-shaped crack. To simulate one representative crack among many, the model is axisymmetric with zero radial displacement at the edge. When the rigid blocks are pulled by a pair of forces, a hydrostatic tension develops in the elastomer. At a critical hydrostatic tension, a small crack deforms substantially, as predicted by an elastic instability, resulting in an unbounded energy release rate. Consequently, the small crack initiates its growth, regardless of the toughness of the elastomer. As the crack grows, the energy release rate decreases, so that the crack arrests. Meanwhile, the rigid blocks constrain deformation of the elastomer far away from the crack, where hydrostatic tension remains high, allowing other cracks to grow. For an elastomer of thickness H, shear modulus μ, and toughness Gc, the crack radius and spacing decrease as the normalized toughness Gc/(μH) increases. Therefore, a tough elastomer of small modulus and thickness will grow numerous small cracks when confined by two rigid blocks and pulled beyond a critical force.



中文翻译:

为什么限制在两个刚性块之间的弹性体层会长出许多空腔?

对于夹在两个刚性块之间的薄层弹性体,当块被拉动时,弹性体中会像裂缝一样生长出许多空腔。为什么弹性体会长出许多小裂纹而不是单个大裂纹?在这里,我们通过分析一个理想模型来回答这个问题,其中弹性体是不可压缩的 neoHookean 材料,并且包含一分钱形裂缝。为了模拟许多裂纹中的一个代表性裂纹,该模型是轴对称的,边缘处的径向位移为零。当刚性块被一对力拉动时,弹性体中会产生静水张力。在临界静水压力下,小裂纹会发生显着变形,正如弹性不稳定性所预测的那样,从而导致无限的能量释放率。因此,小裂纹开始生长,无论弹性体的韧性如何。随着裂纹的增长,能量释放率降低,从而使裂纹停止。同时,刚性块限制了远离裂缝的弹性体的变形,那里的静水张力仍然很高,从而使其他裂缝得以扩展。对于厚度的弹性体H , 剪切模量μ, 和韧性GC,裂纹半径和间距随着归一化韧性的降低而减小GC/(μH)增加。因此,当由两个刚性块限制并拉动超过临界力时,具有小模量和厚度的坚韧弹性体将产生许多小裂缝。

更新日期:2023-01-23
down
wechat
bug