A strain-consistent elastic plate model with surface elasticity

Abstract

A strain-consistent elastic plate model is formulated in which both initial surface tension and the induced residual stress are treated as finite values, and the exactly same strain expressions are consistently employed for both the surface and the bulk plate. Different than most of previous related models which follow the original Gurtin-Murdoch model and include some non-strain displacement gradient terms (which cannot be expressed in terms of the surface infinitesimal strains or the von Karman-type strains) in the surface stressstrain relations, the present model does not include any non-strain displacement gradient terms in the surface stress-strain relations. For a free elastic plate with in-plane movable edges, the present model predicts that initial surface tension exactly cancels out the induced residual compressive stress. On the other hand, if all edges are in-plane immovable, residual stress cannot develop in the plate and the initial surface tension causes a tensile net membrane force. In addition, the present model predicts that initial surface tension reduces the effective bending rigidity of the plate, while this reduction does not depend on Poisson ratio. In particular, self-buckling of a free elastic plate under tensile surface tension cannot occur unless the effective bending rigidity of plate vanishes or becomes negative.

Peculiarities of deformation of round thin-film membranes and experimental determination of their effective characteristics

“…Analysis of membranes, fixed on contour, should be performed considering their geometrical dimensions and actual conditions of fixing, appearing during their manufacture. Significant impact of scale factor, particularly surface energy, change of effective properties, etc., appearing at sizes of several hundreds of nanometersis noted in many studies [6][7][8][9][10][11][12][13][14][15][16][17][18]. Besides, the physico-mechanical aspects of manufacturing process (growth, etching, etc.)…”

Особенности Деформирования Круглых Тонкопленочных Мембран И Экспериментальное Определение Их Эффективных Характеристик

“…Анализ закрепленных на контуре мембран следует осуществлять с учетом их фактических геометрических размеров и реальных условий закрепления, возникающих в процессе их изготовления. Существенное влияние масштабного фактора, в частности, поверхностной энергии, изменения эффективных свойств и др., проявляющееся при размерах порядка нескольких сотен нанометров -отмечено во многих исследованиях [6][7][8][9][10][11][12][13][14][15][16][17][18]. Кроме того, на специфику распределения остаточных напряжений в тонкостенных структурах могут оказывать существенное влияние физико-механические аспекты процесса их создания (роста, травления и пр.)…”

Buckling of an Annular Nanoplate Under Tensil Point Loading

“…It strongly limits the practical applicability of these models. Therefore, along with the complete GM model of the surface elasticity [5,6], the simplified strain-consistent form of the linearized GM relations is used [7,8,9]. It preserves its basic physical essence and, at the same time, allows to reduce the solving equations to the classical structure of the macromechanics equations.…”