论文标题
固体膜的凹痕在刚性底物上具有范德 - 瓦尔人的吸引力
Indentation of solid membranes on rigid substrates with Van-der-Waals attraction
论文作者
论文摘要
我们在平滑的刚性基板中悬挂在半径$ r \ ll r_ {sheet} $的圆形孔上的尺寸$ r_ {sheet} $的薄薄的固体板的凹痕，以解决孔边缘边界条件的影响。引入Van-der-Waals（VDW）的基本理论模型（VDW）板材覆盖吸引力时，我们证明了具有滑动条件的夹紧条件（Schwerin模型）的戏剧性效果，从而使床单的支撑部分可以滑入凹痕并通过Angeclom-Scale-Scale-Scale deftibriment诱导的螺旋式压缩范围，从而逐渐降低互动率，从而确定了脉络范围的范围。我们强调了一种可能性，即压痕力$ f $可能不会表现出对凹痕深度（$ f \ proptoδ^3 $）的普遍预期的依赖，在这种深度上，比例不变的是由床单的拉伸模量和孔的半径$ r $控制的，而是一个{\ emph {psedu $ f priptition $ f.常数由弯曲模量，VDW吸引力和表的大小$ r_ {sheet} \ gg r $控制。
We revisit the indentation of a thin solid sheet of size $R_{sheet}$ suspended on a circular hole of radius $R \ll R_{sheet}$ in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the Van-der-Waals (VdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermodynamic equilibrium (determined by the VdW potential). We highlight the possibility that the indentation force $F$ may not exhibit the commonly anticipated cubic dependence on the indentation depth ($F\propto δ^3$), in which the proportionality constant is governed by the sheet's stretching modulus and the hole's radius $R$, but rather a {\emph{pseduo-linear}} response, $F \propto δ$, whereby the proportionality constant is governed by the bending modulus, the VdW attraction, and the sheet's size $R_{sheet} \gg R$.
