Buckling of spherical shells adhering onto a rigid substrate
Buckling of spherical shells adhering onto a rigid substrate
复制标题
DOI：
10.1140/epje/e2005-00038-5
复制
发表时间：
2005-11-01
影响因子：
1.8
通讯作者：
Kato, T
中科院分区：
文献类型：
--
作者：
Komura, S;Tamura, K;Kato, T
通过弹性能和粘附能之和的数值最小化（共轭梯度法）研究由于范德华吸引力相互作用而粘附在刚性基底上的球壳的变形。变形壳的构象由两个无量纲参数控制，即 C-s/epsilon 和 C-b/epsilon，其中 C-s 和 C-b 分别是拉伸常数和弯曲常数，epsilon 是壳与基底之间范德华势的深度。由于这些参数系统地变化，因此表征了四种不同的变形状态：（i）小变形状态，（ii）圆盘形成状态，（iii）各向同性屈曲状态，以及（iv）各向异性屈曲状态。通过测量变形壳的各种量，我们发现大 C-s/epsilon 和小 C-s/epsilon 分别发生不连续和连续屈曲转变。屈曲转变的这种行为类似于范德华液体或凝胶，我们已经在数值上确定了相关的临界点。采用缩放参数来解释粘附引起的屈曲转变，即从圆盘形成状态到各向同性屈曲状态。我们表明，当压痕长度超过由弹性常数确定的有效壳厚度时，就会发生屈曲转变。这个预测与我们的数值结果非常吻合。此外，压痕长度与其在过渡点处的厚度之间的比率提供了一个与壳尺寸无关的常数（2-3）。在从纳米尺度到宏观尺度的各种实验系统中都观察到了这个通用数。特别是，我们的结果与最近使用微胶囊的压缩实验非常吻合。
Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C-s/epsilon and C-b/epsilon where C-s and C-b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C-s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2-3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.