Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations.The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity.An explicit modified form of the Neumann equations is derived to determine the two contact angles,which is reduced to Young's equation for a liquid droplet on a rigid membrane or to the Neumann equations for a liquid droplet on another liquid substrate.Further implications of the modified Neumann equations are examined by comparison with some previous results reported in the recent literature,particularly considering the ranges of material and geometrical parameters of the liquid droplet-membrane system which have not been recently addressed in the literature.

Geometrical shape of in-plane inclusion characterized by polynomial internal stress field under uniform eigenstrains

The internal stress field of an inhomogeneous or homogeneous inclusion in an infinite elastic plane under uniform stress-free eigenstrains is studied. The study is restricted to the inclusion shapes defined by the polynomial mapping functions mapping the exterior of the inclusion onto the exterior of a unit circle. The inclusion shapes, giving a polynomial internal stress field, are determined for three types of inclusions, i.e., an inhomogeneous inclusion with an elastic modulus different from the surrounding matrix, an inhomogeneous inclusion with the same shear modulus but a different Poisson＇s ratio from the surrounding matrix, and a homogeneous inclusion with the same elastic modulus as the surrounding matrix. Examples are presented, and several specific conclusions are achieved for the relation between the degree of the polynomial internal stress field and the degree of the mapping function defining the inclusion shape.

A simple criterion for finite time stability with application to impacted buckling of elastic columns

The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.