Elasto-Plastic Indentation of Auxetic and Metal Foams

2019 ◽  
Vol 87 (1) ◽  
Author(s):  
N. Kumar ◽  
S. N. Khaderi ◽  
K. Tirumala Rao
Keyword(s):  
Poisson’S Ratio ◽  
Strain Energy ◽  
Metal Foams ◽  
Poisson's Ratio ◽  
Indentation Hardness ◽  
The Finite Element Method ◽  
Yield Strain ◽  
Plastic Dissipation ◽  
Auxetic Materials ◽  
Plastic Indentation

Abstract The elasto-plastic indentation of auxetic and metal foams is investigated using the finite element method. The contributions of yield strain, elastic, and plastic Poisson’s ratio on the indentation hardness are identified. For a given yield strain, when the plastic Poisson’s ratio is reduced from 0.5, the indentation hardness decreases first and then increases. This trend was found to be valid for a wide of yield strains. For yield strains less than 0.08, the hardness of auxetic materials is much larger when compared with materials having positive plastic Poisson’s ratio. As the plastic Poisson’s ratio approaches −1, the elastic deformations dominate over the plastic deformations. The plastic dissipation, when compared with the elastic work, is lower for materials with negative Poisson’s ratio. There is no effect of elastic Poisson’s ratio on the indentation hardness when the plastic Poisson’s ratio is more than −0.8. When the plastic Poisson’s ratio is less than −0.8, the hardness increases with a decrease of elastic Poisson’s ratio. The plastic dissipation per unit strain energy is maximum for materials with vanishing plastic Poisson’s ratio.

Large deformation of TPU re-entrant auxetic structures designed by TO approach

2020 ◽  
pp. 009524432093841
Author(s):  
Bahman Taherkhani ◽  
Ali Pourkamali Anaraki ◽  
Javad Kadkhodapour ◽  
Saeed Rezaei ◽  
Haoyun Tu
Keyword(s):  
Poisson’S Ratio ◽  
Effective Properties ◽  
Poisson's Ratio ◽  
The Finite Element Method ◽  
Penalization Method ◽  
Sensor Field ◽  
Auxetic Materials ◽  
Auxetic Structures ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Auxetic materials are a family of rationally designed artificial structures that have unique effective properties gained from the distribution of the internal architecture rather than of the chemical composition. This article used the modified solid isotropic material with penalization method for topology optimization of 2D re-entrant auxetic structures with different Poisson’s ratios and volume fractions. The obtained structures were verified by the finite-element method (FEM) using the commercial FEM software and also validated by the experimental approach. A good agreement was achieved between the experimental and numerical results. Then, the cell geometry effect on Poisson’s ratio under large tension was investigated. Our study revealed that the location and stiffness of rotation joints are two new parameters affecting Poisson’s ratio value. Poisson’s ratio will decrease by decreasing the stiffness of rotation joints and positioning the rotation joints closer to the middle of the structure. So, from the investigation of the optimizer performance, it was achieved that re-entrant auxetic structures with different Poisson’s ratios could be easily designed by changing just the location of rotation joints. This will be applicable in many applications like sensor field.

scholarly journals Giant negative Poisson’s ratio in two-dimensional V-shaped materials

2021 ◽  
Author(s):  
Xikui Ma ◽  
Jian Liu ◽  
Yingcai Fan ◽  
Weifeng Li ◽  
Jifan Hu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Two Dimensional ◽  
Auxetic Materials ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

scholarly journals Models for evaluating craters morphology, relation of indentation hardness and uniaxial compressive strength via a flat-end indenter

2018 ◽  
Vol 10 (1) ◽  
pp. 289-296 ◽  
Author(s):  
Ligang Zhang ◽  
Xiao Fei Fu ◽  
G. R. Liu ◽  
Shi Bin Li ◽  
Wei Li ◽  
...  
Keyword(s):  
Compressive Strength ◽  
Internal Friction ◽  
Uniaxial Compressive Strength ◽  
Poisson’S Ratio ◽  
Failure Process ◽  
Apex Angle ◽  
Poisson's Ratio ◽  
Percentage Error ◽  
Indentation Hardness ◽  
Angle Of Internal Friction

AbstractIn this work, the intensive theoretical study and laboratory tests are conducted to evaluate the craters morphology via the flat-ended indenter test, relationship of indentation hardness (HRI) and uniaxial compressive strength (UCS). Based on the stress distribution, failure process and Mohr–Coulomb failure criterion, the mathematical mechanical models are presented to express the formation conditions of “pulverized zone” and “volume break”. Moreover, a set of equations relating the depth and apex angle of craters, the ratio of indentation hardness and uniaxial compressive strength, the angle of internal friction and Poisson’s ratio are obtained. The depth, apex angle of craters and ratio of indentation hardness and uniaxial compressive strength are all affected by the angle of internal friction and Poisson’s ratio. The proposed models are also verified by experiments of rock samples which are cored from Da Qing oilfield, the percentage error between the test and calculated results for depth, apex angle of craters and the ratio of HRI and UCS are mainly in the range of –1.41%–8.92%, –5.91%–3.94% and –8.22%–13.22% respectively for siltstone, volcanic tuff, volcanic breccia, shale, sand stone and glutenite except mudstone, which demonstrates that our proposed models are robust and effective for brittle rock.

Buckling and Vibration of Circular Auxetic Plates

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Poisson’S Ratio ◽  
Dynamic Properties ◽  
Elastic Stability ◽  
Buckling Load ◽  
Poisson's Ratio ◽  
Circular Plates ◽  
Critical Buckling Load ◽  
Various Boundary Conditions ◽  
Load Factors ◽  
Auxetic Materials

This paper evaluates the elastic stability and vibration characteristics of circular plates made from auxetic materials. By solving the general solutions for buckling and vibration of circular plates under various boundary conditions, the critical buckling load factors and fundamental frequencies of circular plates, within the scope of the first axisymmetric modes, were obtained for the entire range of Poisson's ratio for isotropic solids, i.e., from −1 to 0.5. Results for elastic stability reveal that as the Poisson's ratio of the plate becomes more negative, the critical bucking load gradually reduces. In the case of vibration, the decrease in Poisson's ratio not only decreases the fundamental frequency, but the decrease becomes very rapid as the Poisson's ratio approaches its lower limit. For both buckling and vibration, the plate's Poisson's ratio has no effect if the edge is fully clamped. The results obtained herein suggest that auxetic materials can be employed for attaining static and dynamic properties which are not common in plates made from conventional materials. Based on the exact results, empirical models were generated for design purposes so that both the critical buckling load factors and the frequency parameters can be conveniently obtained without calculating the Bessel functions.

FLEXURAL RIGIDITY OF THIN AUXETIC PLATES

2014 ◽  
Vol 06 (02) ◽  
pp. 1450012 ◽  
Author(s):  
TEIK-CHENG LIM
Keyword(s):  
Shear Modulus ◽  
Poisson’S Ratio ◽  
Flexural Rigidity ◽  
Poisson's Ratio ◽  
Cube Root ◽  
Square Root ◽  
Isotropic Plates ◽  
Auxetic Materials ◽  
Lower Limits ◽  
Isotropic Solids

The influence of auxeticity on the mechanical behavior of isotropic plates is considered herein by evaluating the plate flexural rigidity as the Poisson's ratio changes from 0.5 to -1. Since the change in plate's Poisson's ratio is followed by a change in at least one of the three moduli, any resulting change to the plate flexural rigidity is only meaningful when at least one of the moduli is held constant. This was performed by normalizing the plate flexural rigidity by a single modulus, a square root of two moduli product, or a cube root of three moduli product to give a dimensionless plate flexural rigidity. It was found that the plate flexural rigidity decreases to a minimum as the plate Poisson's ratio decreases from 0.5 to 0 when only the Young's modulus is held constant. Thereafter the plate flexural rigidity increases with the plate auxeticity. Results also reveal that when only the shear modulus or when the bulk modulus is held constant, the plate flexural rigidity decreases or increases, respectively, with the plate auxeticity. Intermediate trend in the plate flexural rigidity is observed when the product of two moduli is held constant. When the product of all three moduli is held constant, the plate flexural rigidity increases with the plate auxeticity, and the change is especially drastic when the plate Poisson's ratio is near to the upper and lower limits of Poisson's ratio for isotropic solids. Results from this work are useful for structural designers to control the flexural rigidity of plate made from auxetic materials.

Elasto-Plastic Impact on Auxetic/Metal Foams

2020 ◽  
Vol 87 (12) ◽  
Author(s):  
N. Kumar ◽  
S. N. Khaderi ◽  
K. Tirumala Rao
Keyword(s):  
Energy Dissipation ◽  
Impact Velocity ◽  
Poisson’S Ratio ◽  
Metal Foam ◽  
Coefficient Of Restitution ◽  
Peak Force ◽  
Poisson's Ratio ◽  
Rigid Sphere ◽  
Yield Strain ◽  
Maximum Displacement

Abstract We investigate the normal impact of a rigid sphere on a half-space of elasto-plastic auxetic/metal foam using the finite element method. The dependence of the coefficient of restitution, peak force, maximum displacement, and contact duration on the yield strain, impact velocity, and elastic and plastic Poisson’s ratio is analyzed. For a given elastic Poisson’s ratio, the coefficient of restitution generally decreases with an increase in the plastic Poisson’s ratio and impact velocity. When the plastic Poisson’s is maintained constant, the coefficient of restitution increases with an increase of the elastic Poisson’s ratio. These trends are explained using plastic energy dissipation. The energy dissipation trends are further investigated by decomposing it into deviatoric and hydrostatic parts. For a given impact velocity, the peak force is relatively insensitive to most of the elastic and plastic Poisson’s ratio combinations. We also show that for the cases where the elastic and plastic Poisson’s ratios are equal, the coefficient of restitution is relatively insensitive to their actual values. These findings can guide researchers to identify the right elastic and plastic Poisson’s ratio combinations so that lattice materials with exceptional energy absorbing capacity can be designed using topology optimization.

Circular Auxetic Plates

2012 ◽  
Vol 29 (1) ◽  
pp. 121-133 ◽  
Author(s):  
T.-C. Lim
Keyword(s):  
Poisson’S Ratio ◽  
Load Distribution ◽  
Point Load ◽  
Poisson's Ratio ◽  
Circular Plates ◽  
Auxetic Materials ◽  
Edge Conditions ◽  
Bending Stresses ◽  
The Common ◽  
Laterally Loaded

AbstractThis paper investigates the suitability of auxetic materials for load-bearing circular plates. It is herein shown that the optimal Poisson's ratio for minimizing the bending stresses is strongly dependent on the final deformed shape, load distribution, and the type of edge supports. Specifically, the use of auxetic material for circular plates is recommended when (a) the plate is bent into a spherical or spherical-like cap, (b) a point load is applied to the center of the plate regardless of the edge conditions, and (c) a uniform load is applied on a simply-supported plate. However, auxetic materials are disadvantaged when a flat plate is to be bent into a saddle-like shell. The optimal Poisson's ratios concept recommended in this paper is useful for providing an added design consideration. In most cases, the use of auxetic materials for laterally loaded circular plates is more advantageous compared to the use of materials with conventional Poisson's ratio, with other factors fixed. This is achieved through materials-based stress re-distribution in addition to the common practices of dimensioning-based stress redistribution and materials strengthening.

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