超重力作用下软材料薄膜失稳的有限元分析

Finite Element Analysis of Soft Material Film Instability under Hypergravity

软材料在自然界和工业应用中无处不在,其显著特点是对外界刺激极其敏感,相对于传统材料其弹性模量更小,容易发生表面形态的失稳现象.现有研究主要把光、声、电等作为诱导材料失稳的因素进行研究,而重力往往作为常量考虑.本文通过有限元模拟,建立超重力作用下环向受限的圆柱状软材料薄膜失稳模型,探究了薄膜材料的密度、厚度、半径、剪切模量等材料和几何参数对失稳临界超重力和临界失稳模态的影响.结果表明,触发薄膜失稳的超重力随薄膜厚度和密度增大而减小,随剪切模量增大而增大,随着薄膜半径增大快速减小并迅速趋于常数.另外,当径厚比R/H较小时,无量纲临界超重力随着径厚比增大而单调减小,但当径厚比R/H大于3时,此量为一个常数.超重力作用下软材料的临界失稳模态与密度、剪切模量等参数无关,随径厚比R/H增大,临界失稳模态波数增大、波长减小.

Soft materials are omnipresent in nature and industry applications.One of its obvious characteristics is the extreme sensitivity to external stimuli.Compared with traditional hard materials,soft materials have much smaller elastic modulus and are more proneto instability which produces various surface morphologies.In most existing studies,light,sound and electricity etc.were mostly used to induce material instability,while gravity is always considered as a constant.In this paper,finite element simulation is performed to investigate instability behavior of soft elastic circular slab under hypergravity.The influences of material and geometrical parameters such as density,thickness,radius,and shear modulus on the critical hypergravity and mode of instability are examined extensively.The results show that the critical hypergravity that triggers the instability decreases with the thickness and density,but increases with the shear modulus.In addition,dimensionless critical hypergravity decreases monotonically with the radius of the slab for small radius-to-thickness ratio,but keeps constant when the slab radius-to-thickness ratio is larger than R/H≈3.The critical instability mode of soft slab under hypergravity is irrelevant to the parameters of the density and shear modulus.However,as the aspect ratio R/H increases,the critical instability mode wavenumber increases,and the wavelength decreases.