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Short-range correlations control the G/K and Poisson ratios of amorphous solids and metallic glasses
The bulk modulus of many amorphous materials, such as metallic glasses, behaves nearly in agreement with the assumption of affine deformation, namely that the atoms are displaced just by the amount prescribed by the applied strain. In contrast, the shear modulus behaves as for nonaffine deformations, with additional displacements due to the structural disorder which induce a marked material softening to shear. The consequence is an anomalously large ratio of the bulk modulus to the shear modulus for disordered materials characterized by dense atomic packing, but not for random networks with point atoms. We explain this phenomenon with a microscopic derivation of the elastic moduli of amorphous solids accounting for the interplay of nonaffinity and short-range particle correlations due to excluded volume. Short-range order is responsible for a reduction of the nonaffinity which is much stronger under compression, where the geometric coupling between nonaffinity and the deformation field is strong, whilst under shear this coupling is weak. Predictions of the Poisson ratio based on this model allow us to rationalize the trends as a function of coordination and atomic packing observed with many amorphous materials.
Temperature dependence of viscoelastic Poisson’s ratio of cement mortar
Abstract Concrete creep research has focused primarily on uniaxial response. However, biaxially prestressed concrete structures are common, resulting in a multiaxial stress state that can complicate the behavior of a viscoelastic material like concrete. Significant creep strains may be induced in directions transverse to each principle stress due to Poisson’s effect. Past research is unclear regarding the viscoelastic or viscoplastic properties of concrete outside of uniaxial response. It has been reported in separate studies that concrete viscoelastic/viscoplastic Poisson’s ratio (VPR) is an increasing, decreasing and constant function with time, with all reported measurements performed at room temperature. In this paper, the 3D basic creep response of mature cement mortar is examined using a confined compression experiment that allows direct determination of the full stress and infinitesimal strain tensors in a single test, which enables the determination of VPR under a multiaxial stress state. For this purpose, a unique, miniature version of the standardized concrete creep frame is designed that is amenable to placing in climate chambers and temperature ovens. The experimental results indicate that the VPR of sealed, mature cement mortar is nearly constant and equal to the elastic at room temperature, while the VPR gradually increases with time when measured at 60 °C.
Poisson's Ratio of a Hyperelastic Foam Under Quasi-static and Dynamic Loading
Poisson's ratio is a material constant representing compressibility of material volume. However, when soft, hyperelastic materials such as silicone foam are subjected to large deformation into densification, the Poisson's ratio may rather significantly change, which warrants careful consideration in modeling and simulation of impact/shock mitigation scenarios where foams are used as isolators. The evolution of Poisson's ratio of silicone foam materials has not yet been characterized, particularly under dynamic loading. In this study, radial and axial measurements of specimen strain are conducted simultaneously during quasi-static and dynamic compression tests to determine the Poisson's ratio of silicone foam. The Poisson's ratio of silicone foam exhibited a transition from compressible to nearly incompressible at a threshold strain that coincided with the onset of densification in the material. Poisson's ratio as a function of engineering strain was different at quasi-static and dynamic rates. Here, the Poisson's ratio behavior is presented and can be used to improve constitutive modeling of silicone foams subjected to a broad range of mechanical loading.
Parametric estimation of Poisson's ratio for thin hinged-hinged plates
Cornu's method is an elegant calculation besieged by an impractical approach to obtain accurate estimates for Poisson's ratio. Conventionally, Cornu's method requires several components, and each component can adversely affect the accuracy of the measurement. Furthermore, Cornu's conventional method requires a long beam because beams with short length-to-width ratios cause the estimate of Poisson's ratio to diverge from the true value of Poisson's ratio. We believe that, with the right modifications, Cornu's method can become an attractive approach to obtaining precise estimates for Poisson's ratio from mode shapes. Here we use finite element simulations to show how to use Cornu's method to estimate Poisson's ratio from a mode shape. Our modified Cornu's method removes knife-edges and loading components for a hinged-hinged plate under steady-state excitation. Given the true value of Poisson's ratio, as a performance specification, we show that simple parametric expressions can fit estimates for Poisson's ratio for different length-to-width ratios of thin hinged-hinged plates. Additionally, we show that estimates for Poisson's ratio from higher modes align with the results from the first mode and explain our expectation for this outcome. Furthermore, our results challenge the idea that anticlastic, monoclastic, and synclastic deformation uniquely correspond to positive, zero, and negative estimates of Poisson's ratio, respectively. With the emergence of materials-by-design, we expect that this parametric technique will be able to assist in experimental qualification of thin beam and plate structures with respect to the desired value of Poisson's ratio.
Ab Initio Simulation of Structure and Properties in Ni-Based Superalloys: Haynes282 and Inconel740
The electronic structure, interatomic bonding, and mechanical properties of two supercell models of Ni-based superalloys are calculated using ab initio density functional theory methods. The alloys, Haynes282 and Inconel740, are face-centered cubic lattices with 864 atoms and eleven elements. These multi-component alloys have very complex electronic structure, bonding and partial-charge distributions depending on the composition and strength of the local bonding environment. We employ the novel concept of total bond order density (TBOD) and its partial components (PBOD) to ascertain the internal cohesion that controls the intricate balance between the propensity of metallic bonding between Ni, Cr and Co, and the strong bonds with C and Al. We find Inconel740 has slightly stronger mechanical properties than Haynes282. Both Inconel740 and Haynes282 show ductile natures based on Poisson’s ratio. Poisson’s ratio shows marginal correlation with the TBOD. Comparison with more conventional high entropy alloys with equal components are discussed.
Poisson’s ratio of eTPU molded bead foams in compression via in situ synchrotron X-ray microtomography
In situ synchrotron X-ray microtomography was used to characterize the bulk deformation behavior by computing the Poisson's ratio of expanded thermoplastic polyurethane (eTPU) molded bead foams used in footwear midsole during compression. Quantitative data on morphological characteristics were obtained using an iterative image processing workflow. Image correlation on the 4D datasets using DVC was performed to calculate the volumetric and axial strain to estimate the Poisson ratio. Strain maps from DVC showed the influence of variability in ligament thickness distribution on the global mechanical behavior exhibited which dominated the response seen in these bead foams. Lastly, our results showed a strong correlation between Poisson ratio and distribution of ligament thickness in foams.
Poisson's ratio of collagen fibrils measured by small angle X-ray scattering of strained bovine pericardium
Type I collagen is the main structural component of skin, tendons, and skin products, such as leather. Understanding the mechanical performance of collagen fibrils is important for understanding the mechanical performance of the tissues that they make up, while the mechanical properties of bulk tissue are well characterized, less is known about the mechanical behavior of individual collagen fibrils. In this study, bovine pericardium is subjected to strain while small angle X-ray scattering (SAXS) patterns are recorded using synchrotron radiation. The change in d-spacing, which is a measure of fibril extension, and the change in fibril diameter are determined from SAXS. The tissue is strained 0.25 (25%) with a corresponding strain in the collagen fibrils of 0.045 observed. The ratio of collagen fibril width contraction to length extension, or the Poisson's ratio, is 2.1 ± 0.7 for a tissue strain from 0 to 0.25. This Poisson's ratio indicates that the volume of individual collagen fibrils decreases with increasing strain, which is quite unlike most engineering materials. This high Poisson's ratio of individual fibrils may contribute to high Poisson's ratio observed for tissues, contributing to some of the remarkable properties of collagen-based materials.
Understanding the changes in ductility and Poisson's ratio of metallic glasses during annealing from microscopic dynamics
In the paper K. L. Ngai et al., [J. Chem. 140, 044511 (2014)], the empirical correlation of ductility with the Poisson's ratio, ν{sub Poisson}, found in metallic glasses was theoretically explained by microscopic dynamic processes which link on the one hand ductility, and on the other hand the Poisson's ratio. Specifically, the dynamic processes are the primitive relaxation in the Coupling Model which is the precursor of the Johari–Goldstein β-relaxation, and the caged atoms dynamics characterized by the effective Debye–Waller factor f{sub 0} or equivalently the nearly constant loss (NCL) in susceptibility. All these processes and the parameters characterizing them are accessible experimentally except f{sub 0} or the NCL of caged atoms; thus, so far, the experimental verification of the explanation of the correlation between ductility and Poisson's ratio is incomplete. In the experimental part of this paper, we report dynamic mechanical measurement of the NCL of the metallic glass La{sub 60}Ni{sub 15}Al{sub 25} as-cast, and the changes by annealing at temperature below T{sub g}. The observed monotonic decrease of the NCL with aging time, reflecting the corresponding increase of f{sub 0}, correlates with the decrease of ν{sub Poisson}. This is important observation because such measurements, not made before, provide the missing link in confirming by experiment the explanation of the correlation of ductility with ν{sub Poisson}. On aging the metallic glass, also observed in the isochronal loss spectra is the shift of the β-relaxation to higher temperatures and reduction of the relaxation strength. These concomitant changes of the β-relaxation and NCL are the root cause of embrittlement by aging the metallic glass. The NCL of caged atoms is terminated by the onset of the primitive relaxation in the Coupling Model, which is generally supported by experiments. From this relation, the monotonic decrease of the NCL with aging time is caused by the slowing down of the primitive relaxation and β-relaxation on annealing, and vice versa.
Differential Poisson’s ratio of a crystalline two-dimensional membrane
We compute the differential Poisson’s ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality d≫1. We demonstrate that, in the regime of anomalous Hooke’s law, the differential Poisson’s ratio approaches a universal value determined solely by the spatial dimensionality d c , with a power-law expansion ν=-1/3+0.016/d c +O(1/d c 2 ), where d c =d-2. Thus, the value -1/3 predicted in previous literature holds only in the limit d c →∞.
Time-average holographic estimation of Poisson's ratio by Cornu's method from mode shapes
More than 150 years ago, Marie Alfred Cornu first demonstrated his method of using interferometry to directly measure Poisson’s ratio from a radially bent beam. It is an elegant approach to measuring Poisson’s ratio of a beam requiring only two length measurements. Cornu’s method combines the high precision of interferometry with a four-point bending apparatus. This research simulates an interferometry technique called time-average scanning digital holography to make direct estimates of Poisson’s ratio from the antin odes of a mode shape. We show it is possible to make direct estimates of Poisson’s ratio from the antinode of a mode shape although the estimates diverge from the true value of Poisson’s ratio. We find that the di vergence is proportional to the distance between the nodes of a mode shape. We then develop an expression for converting our direct estimate back to within two percent of the true value of Poisson’s ratio for a thin, homogeneous, and hinged-hinged beam, or plate. The remainder of the research seeks to extend this method to combinations of clamped, free, and hinged boundary conditions.
The estimation of Poisson’s ratio by time-averaging and Cornu’s method for isotropic beams
Prior research suggests that direct static (e.g., uniaxial testing) and dynamic (e.g., ultrasonic wave propagation analysis) measurements differ in the estimation of Poisson’s ratio because anisotropies and heterogeneities in the sample material affect the two types of tests differently. Even assuming isotropic and homogeneous material properties, prior research further suggests that discrepancies between static/dynamic test results will exist because the error of the diagnostic techniques for the measurand are inherently different. Finally, thermodynamic effects are not present in static tests but can significantly affect dynamic test results. Given the potential for all these variables to produce discrepancies, it would be helpful to have the measurement of Poisson’s ratio obtainable from the same theory and experimental measurements by either static or dynamic testing methods. Our finite element calculations show that by combining time-averaged scanning digital holography with Cornu’s method, it is theoretically possible to estimate the effective Poisson’s ratio from the anticlastic contours at the antinode of the first out-of-plane bending mode shape. This is true regardless of frequency and therefore applicable for both static and dynamic measurements. Our results show that the estimate of Poisson’s ratio by Cornu’s method using data from simulations of mode shapes approaches the true value of Poisson’s ratio. Additionally, our research suggests that beam geometry and boundary conditions are fundamental factors limiting the convergence of the estimate of Poisson’s ratio to the true value of Poisson’s ratio regardless of performing a static or dynamic test.
ABC -Auxetics: An Implicit Design Approach for Negative Poisson's Ratio Materials
A novel methodology is introduced for designing auxetic (negative Poisson's ratio) structures based on topological principles and is demonstrated by investigating a new class of auxetics based on two-dimensional (2D) textile weave patterns. Conventional methodology for designing auxetic materials typically involves determining a single deformable block (a unit cell) of material whose shape results in auxetic behavior. Consequently, patterning such a unit cell in a 2D (or 3D) domain results in a larger structure that exhibits overall auxetic behavior. Such an approach naturally relies on some prior intuition and experience regarding which unit cells may be auxetic. Second, tuning the properties of the resulting structures is typically limited to parametric variations of the geometry of a specific type of unit cell. Thus, most of the currently known auxetic structures belong to a selected few classes of unit cell geometries that are explicitly defined in accordance with a specified topological (i.e., grid structure). Herein, a new class of auxetic structures is demonstrated that, while periodic, can be generated implicitly, i.e., without reference to a specific unit cell design. The approach leverages weave-based parameters (A–B–C), resulting in a rich design space for auxetics that is previously unexplored.
Exploiting negative Poisson's ratio to design 3D-printed composites with enhanced mechanical properties
Auxetic materials exhibiting a negative Poisson's ratio are shown to have better indentation resistance, impact shielding capability, and enhanced toughness. Here, we report a class of high-performance composites in which auxetic lattice structures are used as the reinforcements and the nearly incompressible soft material is employed as the matrix. This coupled geometry and material design concept is enabled by the state-of-the-art additive manufacturing technique. Guided by experimental tests and finite element analyses, we systematically study the compressive behavior of the 3D printed auxetics reinforced composites and achieve a significant enhancement of their stiffness and energy absorption. This improved mechanical performance is due to the negative Poisson's ratio effect of the auxetic reinforcements, which makes the matrix in a state of biaxial compression and hence provides additional support. This mechanism is further supported by the investigation of the effect of auxetic degree on the stiffness and energy absorption capability. The findings reported here pave the way for developing a new class of auxetic composites that significantly expand their design space and possible applications through a combination of rational design and 3D printing.
Negative Poisson’s Ratio in 1T-Type Crystalline Two-Dimensional Transition Metal Dichalcogenides
Materials with a negative Poisson’s ratio, also known as auxetic materials, exhibit unusual and counterintuitive mechanical behaviour—becoming fatter in cross-section when stretched. Such behaviour is mostly attributed to some special re-entrant or hinged geometric structures regardless of the chemical composition and electronic structure of a material. Here, using first-principles calculations, we report a class of auxetic single-layer two-dimensional materials, namely, the 1T-type monolayer crystals of groups 6–7 transition-metal dichalcogenides, MX 2 (M=Mo, W, Tc, Re; X=S, Se, Te). These materials have a crystal structure distinct from all other known auxetic materials. They exhibit an intrinsic in-plane negative Poisson’s ratio, which is dominated by electronic effects. We attribute the occurrence of such auxetic behaviour to the strong coupling between the chalcogen p orbitals and the intermetal t 2g -bonding orbitals within the basic triangular pyramid structure unit. In conclusion, the unusual auxetic behaviour in combination with other remarkable properties of monolayer two-dimensional materials could lead to novel multi-functionalities.
Observations of how boundary conditions affect estimates of Poisson's ratio from simulated mode shapes
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Bond-Based Peridynamics: a Tale of Two Poisson’s Ratios
This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in Gerstle et al. (2005) wherein for isotropic materials a Poisson’s ratio restriction of $\frac{1}{4}$ for plane strain and $\frac{1}{3}$ for plane stress is deduced. Next, we show Cauchy’s relations are an intrinsic limitation of bond-based peridynamics and specialize these restrictions to plane strain and plane stress models. This generalizes the results from Gerstle et al. (2005) and demonstrates that the Poisson’s ratio restrictions described in Gerstle et al. (2005) are merely a consequence of Cauchy’s relations for isotropic materials. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.
Elastic constants determined by nanoindentation for p-type thermoelectric half-Heusler
This paper presents a study of the elastic properties of the p-type thermoelectric half-Heusler material, Hf{sub 0.44}Zr{sub 0.44}Ti{sub 0.12}CoSb{sub 0.8}Sn{sub 0.2}, using nanoindentation. Large grain-sized polycrystalline specimens were fabricated for these measurements, providing sufficient indentation targets within single grains. Electron Backscatter Diffraction methods indexed the target grains for the correlation needed for our elastic analysis of individual single crystals for this cubic thermoelectric material. Elastic properties, including the Zener ratio and the Poisson ratio, obtained from the elasticity tensor are also reported.