Effects of Poisson's ratio on the deformation of thin membrane structures under indentation

Abstract

Deformation/deflection of thin shells/membranes with clamped boundaries is a common material behaviour relevant to many engineering and medical conditions. A detailed understanding of the deformation mechanisms of different materials/structures with different Poisson's ratios under such a loading condition is of great significance to materials testing and product development. In this work, the deformation of circular elastic membranes with a clamped edge under point loading and finite contact conditions is systematically studied incorporating auxeticity behaviours. The effect of Poisson's ratio on the deformation of the material is investigated and the influence of parameters including sample thickness, indentation depth and indenter size is analysed. The feasibility and limitation of an analytical solution is evaluated. The work shows that the P/δ3 relationship is applicable to describe the force–displacement data over the membrane domain for both point loading and finite contact conditions. It is shown that negative Poisson's ratios have direct influence on the membrane deformation domain, including the force–displacement curve, the deflection profile and the contact area. Critical factors affecting the P–h curves and the deformation mechanisms are discussed with reference to potential use of the Poisson's ratio effects.

The Effects of Poisson's Ratio on the Indentation Behavior of Materials With Embedded System in an Elastic Matrix

“…With higher stiffness values for the embedment layer, a linear relationship is observed between the stiffness of the layer and the indentation stiffness ratio. Similarly, a linear relationship is found between the thickness of embedded layer and the indentation stiffness ratio (Figure ), which is similar to the case for a free standing membrane with fixed boundary conditions …”

“…Similarly, a linear relationship is found between the thickness of embedded layer and the indentation stiffness ratio (Figure 9), which is similar to the case for a free standing membrane with fixed boundary conditions. [38] Apart from the influence of auxeticity on the indentation resistance ratio, the deformation and stresses of the embedment, is also important, as it may influence the function of the embedment. Figure 11 compares the displacement fields (a-c) and maximum principal in-plane stresses of the embedded layer (d) between matrix with positive and negative Poisson's ratios.…”

“…It is well documented that, negative Poisson's ratio influences the material deformation under localised deformation such as indentation . Most of the earlier work has been focused on foam structures, while recent investigation/predictions on the isotropic auxetic materials have increased with the development of new auxetic material systems at different scales . A recent study performed by Argatov et al investigated indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint, the effect of Poisson's ratio and auxeticity is found to be dependent on the shape of the indenter, a stronger effect of Poisson's ratio for a flat ended indenter than that for a spherical indenter is predicted.…”

“…[31][32][33] Most of the earlier work has been focused on foam structures, while recent investigation/predictions on the isotropic auxetic materials have increased with the development of new auxetic material systems at different scales. [34][35][36][37][38] A recent study performed by Argatov et al [37] investigated indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint, the effect of Poisson's ratio and auxeticity is found to be dependent on the shape of the indenter, a stronger effect of Poisson's ratio for a flat ended indenter than that for a spherical indenter is predicted. Furthermore, Photiou et al [33] illustrated via theoretical analysis and numerical modeling, that the negative Poisson's ratio has much stronger influence on the normalised hardness than the positive Poisson's ratio.…”

An Accurate Design Equation for the Maximum Deflection in a Class of Auxetic Sectorial Plates

“…For a comprehensive survey on auxetic materials and structures, the reader is referred to a recent review and monograph. [27,28] While the early and subsequent years of auxetic research has been performed on micromechanical modeling to understand the structure-property-processing relationships that give rise to auxetic behavior in bulk solids, there has been an increasing trend toward effort to comprehend the effect of auxeticity on membranes, [29][30][31] rods, [32][33][34] beams, [35][36][37] shells, [38][39][40] and plates. [41][42][43][44] In the case of plates, the effect of material auxeticity has been investigated on problems of the following mechanical nature: a) static, [45][46][47][48] b) dynamic, [49][50][51][52][53][54] c) thermoelasticity and/or thermal stresses, [55][56][57][58][59] d) instability, [59][60][61][62] e) first-order and higher-order shear deformation, [62][63][64][65][66][67] as well as f) plates of unconventional shapes.…”