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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.
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.
Observations of how boundary conditions affect estimates of Poisson's ratio from simulated mode shapes
Not Available
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.
Pressure dependence of Poisson’s ratio of glassy Baltic amber studied by Brillouin scattering spectroscopy
Amber is a typical natural glass with very long aging time. Elastic properties of amber at high pressures have been studied using Brillouin scattering and a diamond anvil cell. Both longitudinal and transverse acoustic modes have been observed up to 12 GPa. The pressure dependences of longitudinal, shear, Young’s, and bulk moduli, compressibility, and Poisson’s ratio were determined. The longitudinal, shear, Young’s, bulk moduli show the remarkable increase, and compressibility shows a marked decrease with increasing pressure. However, it is found that the pressure dependence of Poisson’s ratio is very small. The mechanism of this small pressure dependence was discussed. Finally, the Cauchy type relation between longitudinal and shear moduli was examined. Its coefficients show the deviation from the Cauchy relation owing to the coexistence of different intermolecular interactions in amber.
A Coherently Strained Monoclinic [111]PbTiO 3 Film Exhibiting Zero Poisson's Ratio State
Abstract [111]‐Oriented perovskite oxide films exhibit unique interfacial and symmetry breaking effects, which are promising for novel quantum materials as topological insulators and polar metals. However, due to strong polar mismatch and complex structural reconstructions on (111) surfaces/interfaces, it is still challenging to grow high quality [111] perovskite heterostructures, let alone explore the as‐resultant physical properties. Here, the fabrication of ultrathin PbTiO 3 films grown on a SrTiO 3 (111) substrate with atomically defined surfaces, by pulsed laser deposition, is reported. High‐resolution scanning transmission electron microscopy and X‐ray diffraction reveal that the as‐grown [111]PbTiO 3 films are coherent with the substrate and compressively strained along all in‐plane directions. In contrast, the out‐of‐plane lattices are almost unchanged compared with that of bulk PbTiO 3 , resulting in a 4% contraction in unit cell volume and a nearly zero Poisson's ratio. Ferroelectric displacement mapping reveals a monoclinic distortion within the compressed [111]PbTiO 3 , with a polarization larger than 50 µC cm −2 . The present findings, as further corroborated by phase field simulations and first principle calculations, differ significantly from the common [001]‐oriented films. Fabricating oxide films through [111] epitaxy may facilitate the formation of new phase components and exploration of novel physical properties for future electronic nanodevices.
Elasticity, Anisotropy and Magnetism of Anti-perovskite M{sub 3}AlC (M=Ti, Fe, Sm) from First-Principle Calculations
Elasticity, anisotropy, and magnetism of anti-perovskite M{sub 3}AlC (M=Ti, Fe, Sm) have been calculated and investigated via non-relativistic density functional theory. And the elasticity constant, elastic modulus, Poisson ratio, and Cauchy pressure of three structures have been obtained. Based on the Poisson ratio, Pugh modulus ratio, and Cauchy pressure, bonding attributes of the three materials have been analyzed. The result showed that Ti{sub 3}AlC is a brittle material with high degrees of strength, rigidity, and hardness, and Sm{sub 3}AlC and Fe{sub 3}AlC possess excellent toughness. Based on the universal elastic anisotropy index A{sup U}, anisotropy fraction ratios A{sub B}, A{sub G}, and A{sub E},and Zener factor A, it showed that all three M{sub 3}AlC structures demonstrated elasticity and anisotropy. The elasticity and anisotropy of the three M{sub 3}AlC structures has been illustrated in three-dimensional images of the elastic modulus. Compared with Ti{sub 3}AlC and Fe{sub 3}AlC, Sm{sub 3}AlC has a significantly higher level of anisotropy. Moreover, in this paper, the magnetism of transition metal Fe and rare earth element Sm in the M{sub 3}AlC structure has been compared and analyzed from the perspective of the electronic structure and population analysis.
Anomalous elasticity, fluctuations and disorder in elastic membranes
Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic “membrane” embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d→∞, (ii) D→4, and (iii) D=d. Focusing on the critical “flat” phase, for a homogeneous two-dimensional (D=2) membrane embedded in three dimensions (d=3), we predict its universal roughness exponent ζ=0.590, length-scale dependent elastic moduli exponents η=0.821 and η{sub u}=0.358, and an anomalous Poisson ratio, σ = - 1/3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ'=0.775,η' = 0.449,η{sub u}'=1.101 and a Poisson ratio σ ' = - 1/3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a “phantom” sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν=0.732 and η=0.535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene.
A hybrid calibration approach to Hertz-type contact parameters for discrete element models
This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.