任意轴对称弹性体吸附接触的广义Maugis模型
A generalized maugis model for adhesive contact of arbitrary axisymmetric elastic objects
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摘要: 通过线性叠加Sneddon方法和Lowengrub-Sneddon方法分别给出的解, 得到了一个弹性半空间轴对称混合边值问题的一般解,进而研究了两个一般轴对称弹性体的正向无摩擦吸附接触问题. 考虑任意有效的表面形状(要求中心部分首先进入接触)和任意的表面吸附作用,推广得到了广义Maugis模型. 该模型是一个半解析的模型,它可以分解成表面形状和表面吸附作用的分别独立影响的两部分,以及一个关联变形和吸附作用的式子. 利用Dugdale模型近似表面吸附作用,得到了具有任意有效的表面形状的广义M-D模型. 它在强吸附或软材料条件下的极限形式是广义JKR模型,而在弱吸附或硬材料下的另一个极限形式是广义DMT模型.Abstract: Based on a linear combination of the solutions derived fromthe Sneddon method and the Lowengrub-Sneddon method, a general solution ofthe axisymmetric problem is obtained for the elastic half-space with mixedboundary conditions. And then, the frictionless and adhesive contact problembetween two general axisymmetric elastic objects is studied. For anarbitrary effective surface profile, i.e., the initial contact occurs at thecentral part, and an arbitrary surface adhesive interaction, a generalizedMaugis model is derived and it can be divided into two parts correspondingto the contributions of the surface profile and the surface adhesiveinteraction, respectively, and a coupling relation between the deformationand the adhesive interaction. Based on the Dugdale model for the surfaceadhesive interaction, a generalized M-D model is derived for an arbitraryeffective surface profile. Two extremes are found for this model. For ashort-range strong interaction or compliant material, its limiting form iscorresponding to the generalized JKR model. And for a long-range weakinteraction or stiff material, another limiting form is corresponding to ageneralized DMT model.
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Keywords:
- adhesion /
- contact /
- generalized M-D model /
- generalized JKR model /
- generalized DMT model
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