In-plane Elastic Constants Research Articles

Lamb wave measurement method for in-plane elastic constants of balanced symmetric laminates based on machine learning

Lamb wave measurement method for in-plane elastic constants of balanced symmetric laminates based on machine learning

Analytical investigation of in-plane and out-of-plane elastic properties of bone-inspired cellular structures

Determining the elastic moduli of materials plays an important role in solving many structural problems, such as vibration and buckling analyses of advanced laminate plates and shells. Bone-inspired cellular structure material (BCS) is a new cellular structure material that has recently attracted the attention of scientists and engineers. However, till now, none of the works in the literature can fully provide the elastic moduli of the BCS. To address these limitations and answer the question of how many elastic constants of BCS are and how to determine all the elastic constants of this material, analytical models are developed in this paper. Here, the analytical models are derived by taking the bending and axial stretching/compression and out-of-plane average normal and shear stress/strain deformation mechanisms in the analysis. We found that the BCS material is orthotropic material with nine independent elastic modulus, including four in-plane elastic constants and five out-of-plane elastic constants. Using the developed analytical models, numerical results are then provided. The accuracy of proposed method is confirmed by the previous obtained results in the literature. Further, in this work we have investigated the influence of the geometry parameters on the elastic properties of the considered bone-inspired cellular structure materials also.

Elastic properties and mechanical stability of bilayer graphene: molecular dynamics simulations

Graphene has become in last decades a paradigmatic example of two-dimensional and so-called van-der-Waals layered materials, showing large anisotropy in their physical properties. Here, we study the elastic properties and mechanical stability of graphene bilayers in a wide temperature range by molecular dynamics simulations. We concentrate on in-plane elastic constants and compression modulus, as well as on the atomic motion in the out-of-plane direction. Special emphasis is placed upon the influence of anharmonicity of the vibrational modes on the physical properties of bilayer graphene. We consider the excess area appearing in the presence of ripples in graphene sheets at finite temperatures. The in-plane compression modulus of bilayer graphene is found to decrease for rising temperature, and results to be higher than for monolayer graphene. We analyze the mechanical instability of the bilayer caused by an in-plane compressive stress. This defines a spinodal pressure for the metastability limit of the material, which depends on the system size. Finite-size effects are described by power laws for the out-of-plane mean-square fluctuation, compression modulus, and spinodal pressure. Further insight into the significance of our results for bilayer graphene is gained from a comparison with data for monolayer graphene and graphite.Graphic abstract

Electronic structure and elasticity of two-dimensional metals of group 10: A DFT study

The discovery of two-dimensional (2D) iron monolayer in graphene pores stimulated experimental and computational material scientists to investigate low-dimensional elemental metals. There have been many advances in their synthesis, stability, and properties in the last few years. Inspired by these advancements, we investigated the electronic structure and elasticity of free-standing monolayers of group 10 elemental metals, viz. Ni, Pd, and Pt. Using density-functional theory (DFT), we explored the energetic, geometric, electronic, and elastic properties of hexagonal, honeycomb, and square lattice structures of each element, in both planar and buckled forms. Among planar configurations, the order of increasing stability is honeycomb, square, and hexagonal. In buckled form, this ordering remains the same for Pt but is reversed for Ni and Pd. Upon geometrical optimization, the extent of buckling for Pt was found to be small compared to Ni and Pd. The effect of buckling on the electronic structure was further scrutinized through the projected density of states, and it was found that highly buckled configurations derive their of states from 3D bulk, which highlights the correlation between buckled configurations and 3D bulk. For Pt in buckled square and honeycomb lattices, the density of states correlates more closely to their 2D monolayers. Regarding elasticity, the in-plane elastic constants indicate that all planar and buckled square lattices are unstable.

Electronic, mechanical and optical properties of the new 1T dipolonide PdPo2 and PtPo2 monolayers: A comparative study with 1T Pd and Pt-based dichalcogenides

We report the electronic, mechanical, and optical properties of the new 1T PdPo 2 and PtPo 2 pristine monolayers, which display a metallic behavior. In the vicinity of the Fermi level, the contributions to the density of states stem from the p z orbitals of Po and the d -states of Pd (Pt). The 2D structures are dynamically stable, showing positive frequencies, except for insignificant negative values in the neighborhood of the Γ point in PtPo 2 . The three lowest optical modes are distinguished by non-vibrating Pd and Pt atoms. Positive in-plane elastic constants indicate the systems’ mechanical stability. Compared to other transition metal dichalcogenides (TMDs), the dipolonides are the most malleable. Our new structures are also thermally stable, showing slight distortions of the trigonal environment but no bond breaking or structural destruction up to a 900 K temperature. The absorption coefficients are non-zero at the infrared level for polarized light along the in-plane directions. This feature is absent in other TMDs, due to their semiconducting aspect. The in-plane reflectivities are also high in this regime. Along the direction perpendicular to the plane of the structures, the 1T PtPo 2 shows a larger maximum reflectivity in the ultraviolet region. This implies that it can, in principle, be appropriately harnessed to serve as both infrared and ultraviolet shield covers. • 1T-PdPo 2 and PtPo 2 monolayers are metallic, contrary to other Pd and Ptbased dichalcogenides. • Mechanically and thermally stable at ambient temperatures. • More malleable than other Pd and Pt-based dichalcogenides. • Absorb/emit light at the infrared/ultraviolet levels making them suitable for optoelectronic devices.

Mechanical behaviors of a novel auxetic honeycomb characterized by re-entrant combined-wall hierarchical substructures

The current focus of the metamaterials is to further improve their performance by the unit cell innovation, while for the auxetic metamaterials, the compromise between the mechanical properties and auxetic effect still needs more efforts. Given this issue, here we developed a novel auxetic honeycomb, named re-entrant combined-wall (RCW) honeycomb, by introducing four hierarchical substructures to the RE cell. Analytical expressions were derived and used to study the in-plane elastic constants of the RCW honeycomb, which were well confirmed by the established finite element model. Further, we investigated its crushing behaviors under large deformation by the explicit numerical method, and the quasi-static crushing experiments were also carried out by the 3D-printed specimens. Results show that the properties of the proposed RCW honeycomb have a high degree of orthogonality and tunability. Compared with the traditional RE honeycomb, the Young’s modulus of the RCW honeycomb in the y direction increases by more than 120%, and the Poisson’s ratio decreases by about 43%. Besides, behaviors of the cell wall contact induced by the adding substructure can lead to an interesting stress enhancement phenomenon under large deformation, which significantly increases its crushing strength, up to 140%, compared with the RE honeycomb. Therefore, the results in this work effectively demonstrate the improved mechanical properties and auxetic performance of the proposed RCW honeycomb. Besides, the adopted design strategy of hierarchical substructure also exhibits great potential for developing novel and excellent auxetic mechanical metamaterials.

In-plane elasticity of beetle elytra inspired sandwich cores

The Beetle Elytron Plate (BEP) is a new class of biomimetic sandwich core that features excellent compressive strength, energy absorption capacity and flexural properties. These characteristics make BEPs suitable as potential replacements of classical honeycomb cores in sandwich panels. This work describes the behaviour of the in-plane engineering elastic constants of parametric BEP topologies for the first time. The beetle elytron cores configurations are simulated using Finite Element models, including full-scale models and representative unit cells with periodic boundary conditions for asymptotic homogenization. The models are also benchmarked against experimental results obtained from ASTM tensile tests related to the in-plane Young’s modulus, Poisson’s ratio and shear modulus. The benchmarked models are then used to perform a parametric analysis against the geometry characteristics of the cellular configurations. Results obtained from this work will provide a solid foundation for further research on BEP structures and expand their applications into wider engineering fields.

Predicting a novel two-dimensional BN material with a wide band gap

Based on density functional theory, a new two-dimensional boron nitride, Pmma BN, is proposed and studied in detail for the first time. The stability of Pmma BN is demonstrated by phonon spectra, ab initio molecular dynamics simulations at 300 and 500 K, and in-plane elastic constants. The orientation dependences of the Young’s modulus and Poisson’s ratio show that Pmma BN has large mechanical anisotropy. Pmma BN is an indirect band gap semiconductor material with a band gap of 5.15 eV, and the hole and electron effective mass have high anisotropy. The electron carrier mobility of Pmma BN along the x and y directions is similar, while the hole carrier mobility along the y direction is more than twice that along the x direction. By studying the effect of uniaxial tensile strain on Pmma BN, the band gap of Pmma BN remains indirect under the uniaxial strain, and its adjustable range reaches 0.64 eV at uniaxial strain along the x direction. When uniaxial strain is applied along the y direction, the positions of the conduction band minimum and valence band maximum change. Pmma BN under uniaxial strain show strong optical absorption capacity in the ultraviolet region. To explore clean energy applications, the thermoelectric properties are also investigated.

Large piezoelectric response in ferroelectric/multiferroelectric metal oxyhalide MOX2 (M = Ti, V and X = F, Cl and Br) monolayers.

Flexible two-dimensional (2D) piezoelectric materials are promising for applications in wearable electromechanical nano-devices such as sensors, energy harvesters, and actuators. A large piezo-response is required for any practical applications. Based on first-principles calculations, we report that ferroelectric TiOX2 and multiferroelectric VOX2 (X = F, Cl, and Br) monolayers exhibit large in-plane stress (e11) and strain (d11) piezoelectric coefficients. For example, the in-plane piezo-response of TiOBr2 (both e11 = 28.793 × 10-10 C m-1 and d11 = 37.758 pm V-1) is about an order of magnitude larger than that of the widely studied 1H-MoS2 monolayer, and also quite comparable to the giant piezoelectricity of group-IV monochalcogenide monolayers, e.g., SnS. Moreover, the d11 of MOX2 monolayers - ranging from 29.028 pm V-1 to 37.758 pm V-1 - are significantly higher than the d11 or d33 of commonly used 3D piezoelectrics such as w-AlN (d33 = 5.1 pm V-1) and α-quartz (d11 = 2.3 pm V-1). Such a large d11 of MOX2 monolayers originates from low in-plane elastic constants with large e11 due to large Born effective charges (Zij) and atomic sensitivity to an applied strain. Moreover, we show the possibility of opening a new way of controlling piezoelectricity by applying a magnetic field.

Homogenization of the macroscopic stiffness of 2D triaxially braided composites: Roles of the local stiffness model and undulating average scheme

This work investigates a two-level homogenization of the macroscopic stiffness of the 2DTBC with emphasizes on the roles of the local stiffness model and undulating average scheme. The effective elastic property of the braid yarn is rigorously derived by an energy method instead of intuitive mathematical average methods in the literature. General formulations of the compliance and stiffness undulating average schemes have been obtained, which are proven to be reduced to the simple mathematical average methods in certain cases. Validated with different experiments, it is unexpected to find out that the prediction combined with the simple rule of mixture and stiffness undulating average scheme yields the most consistent agreement with experimental results after the overall assessment of all the in-plane engineering elastic constants under various braiding conditions.

Concurrence of negative in-plane piezoelectricity and photocatalytic properties in 2D ScAgP2S6 monolayers

Apart from poly(vinylidene fluoride) and its copolymers, 2D multilayered CuInP2S6 (CIPS) is experimentally known to show negative out-of-plane piezoelectric coefficient (d 33) [2019 Sci. Adv. 5 1–10], which is attributable to weak interlayer van der Waals binding. However, CIPS monolayers exhibit positive in-plane piezoelectricity (d 11) [Phys. Status Solidi RRL, 14 2000321], as per DFT calculations. We ascribe it to strong in-plane interatomic bonding. Weakening of the in-plane interatomic bonding may even induce a negative in-plane piezoelectric coefficient, which is exceptionally rare, as observed in this work based on DFT calculations. Much smaller in-plane elastic constants found in ScAgP2S6 monolayers relative to that in CIPS monolayers indicate much weaker in-plane interatomic bonding, which induces negative in-plane piezoelectric coefficient, d 22 = −2.81 pm V−1, in ScAgP2S6 monolayers. In addition to its all-around stability, ScAgP2S6 monolayer is a semiconducting showing a bandgap of 2.04 eV, thereby making it suitable for electronics and solar energy harvesting. Upon the application of 4% biaxial strain on this flexible and stretchable 2D material, d 22 has been found to be drastically increased to −591 pm V−1. The factors causing such an enhancement in d 22 have been ascertained through the maximum rise in the Born effective charges and maximum drop in the elastic constants. With the further drop in elastic constants relative to ScAgP2S6 monolayer, d 22 reaches −3.45 pm V−1 and −13.48 pm V−1 in ScAgP2Se6 and ScAgP2Te6 monolayers respectively. 2D ScAgP2S6 monolayer is found to be a promising photocatalyst as well, since its band edges straddle the water redox potential over the entire range in pH (0–14), in addition to having a high absorption coefficient (≈105 cm−1) in the visible region. It is understood that 2D ScAgP2S6 will substantially expand the scope for its applications in piezoelectricity and visible light harvesting at the nanoscale.

Oxygen-terminated M4X3 MXenes with superior mechanical strength

Two-dimensional (2D) transition metal carbides and nitrides, known as MXenes, have gained notable attention recently because these super-strong materials have many promising applications. In this study, computational analysis is conducted to explore the in-plane elastic constants, 2D stiffness and shear modulus of oxygen terminated M4X3 MXenes by means of the density functional theory (DFT) calculations. Our results reveal that the binding site of the oxygen atoms can greatly affect the mechanical properties. The crystal orbital Hamilton population (COHP) analysis suggests that the impact of the oxygen-binding site is because the M − O bonding strength can significantly influence their mechanical stiffness. Our outcomes may, therefore, provide the theoretical foundation for the advance of MXene-based applications in mechanical engineering.

A novel two-dimensional sp-sp2-sp3 hybridized carbon nanostructure with a negative in-plane Poisson ratio and high electron mobility

A novel two-dimensional (2D) semiconducting carbon allotrope is proposed by inserting alkyne into tetrahexcarbon. This new carbon allotrope consists of tetra-rings and acetylenic linkages and is called TAL-carbon. To the best of our knowledge, this is the first 2D carbon allotrope composed of sp-sp2-sp3 hybridized carbon atoms. Due to its unique puckered structure, TAL-carbon is the fourth 2D carbon material with an intrinsic in-plane negative Poisson ratio (NPR) reported after graphene, penta-graphene, and tetrahexcarbon. Materials with NPR exhibit a wide range of potential applications in biomedicine, aerospace industries, and precision instruments. TAL-carbon has an indirect band gap of 1.614 eV. At room temperature, it exhibits high in-plane electron mobility of up to ~3.5 × 104 cm2V−1s−1, which is 30 times higher than monolayer black phosphorus and two orders of magnitude higher than monolayer MoS2. The phonon dispersion curves and in-plane elastic constants indicate that TAL-carbon is dynamically and mechanically stable. Its equibiaxial strain limit reaches 13.7%, similar to that of graphene. An ab initio molecular dynamics (AIMD) simulation demonstrates that TAL-carbon is thermally stable at 300 K and 1000 K. The results show that TAL-carbon is a promising 2D auxetic material for applications in nanomechanics and nanoelectronics.

Closed-form orthotropic constitutive model for aligned square array mesostructure

This work models the square array mesostructure found in fused filament fabrication parts using an orthotropic constitutive model and derives closed-form expressions for all nine effective elastic constants. The periodic void shape is modeled using a four point hypotrochoid curve with a single shape parameter that controls the sharpness of the points. In-plane elastic constants (Eyy, Ezz, vyz, Gyz) are derived by solving the 2D elasticity equations using the complex variable method of elasticity. The antiplane shear constants (Gxy and Gxz) are derived from a complex variable formulation of the antiplane shear equations. The remaining elastic constants (Exx, vxy, and vxz) are derived by directly solving the linearelasticity equations. We compare our results to unit cell finite element simulations. The simulations match the closed-form expressions exactly for Exx, vxy, and vxz. For the remaining elastic constants, the difference between closed-form model and simulation increases as porosity increases. Tensile testing specimens at various porosity values under 12% are fabricated to test six of the nine elastic constants. Experiments on Exx, vxy, and vxz agree well with closed-form predictions, differing by less than 2.6% for the tested specimen types. Experiments on Eyy, Ezz, and Gxy generally agree well, with larger differences at higher porosity values. The difference is less than 6% for all tested specimen types except for the Ezz specimen with a porosity of 0.113, which had a difference of 21%. Several reasons for the discrepancy are postulated, including non-ideal void shape and interfacial bond stiffness.

Elastic Constants Prediction of 3D Fiber-Reinforced Composites Using Multiscale Homogenization

This paper presents a multi-scale-homogenization based on a two-step methodology (micro-meso and meso-macro homogenization) to predict the elastic constants of 3D fiber-reinforced composites (FRC). At each level, the elastic constants were predicted through both analytical and numerical methods to ascertain the accuracy of predicted elastic constants. The predicted elastic constants were compared with experimental data. Both methods predicted the in-plane elastic constants “ E x ” and “ E y ” with good accuracy; however, the analytical method under predicts the shear modulus “ G x y ”. The elastic constants predicted through a multiscale homogenization approach can be used to predict the behavior of 3D-FRC under different loading conditions at the macro-level.

Mechanical properties of transparent high strength biocomposites from delignified wood veneer

Transparent wood (TW) based on delignified birch veneer and thermoplastic poly(methyl methacrylate) (PMMA) is investigated by uniaxial tensile tests and full-field strain analyses based on digital image correlation techniques. TW is considered as a composite of unidirectional fibers (wood veneer) in a matrix (PMMA). Four in-plane elastic constants along the material axes are reported to enable the usage of continuum mechanics and lamination theory. Longitudinal composite strength is as high as 270 MPa at a reinforcement content of only 25 vol%. The failure behavior is interpreted based on strain field development. Strong reinforcement effects were observed from delignified birch veneer. Despite the fragility of delignified veneers, this constituent provides unexpectedly high reinforcement due to the high cellulose content and favorable stress transfer mechanisms.

In-plane elastic properties of a 2D chiral cellular structure with V-shaped wings

A 2D chiral cellular structure, the unit cell of which is composed of four V-shaped wings, is studied through the energy-based method. The closed-form solutions of the in-plane elastic constants are obtained as functions of geometric parameters and verified through finite element analysis. Furthermore, the influences of geometric parameters on the elastic constants are discussed. Results show that the equivalent moduli of the structure can be several orders of magnitude lower than those of the base material, and the maximum global strains can be dozens of times those of the base material. Besides, the structure shows significant in-plane elastic coupling effects: (1) the maximum ratio of the shear to elastic strain beyond 17.2°/% and (2) the maximum ratio of the elastic to shear strain exceeding 1.52%/° (x-direction) and 1.64%/° (y-direction). As a distinctive 2D chiral cellular structure, the structure shows great potential as a candidate selection for flexible structures in engineering applications.

In-plane elastic constants of a new curved cell walls honeycomb concept

Abstract This paper is focused on the identification of the in-plane elastic constants of a new design of auxetic (negative Poisson's ratio) honeycomb configuration with curved cell walls by using analytical and numerical homogenization techniques. The sensitivity of the elastic constants is determined against the various cell geometry parameters. Good agreement between the analytical and numerical simulations is observed. We show that the specific curved wall honeycomb configuration proposed in this paper possesses a high in-plane shear compliance, tailored anisotropy and the possibility of inducing a negative Poisson's ratio behaviour in baseline honeycomb configurations that would have otherwise positive in-plane Poisson's ratios.

Crack face sliding displacement (CSD) as an input in exact GLOB-LOC expressions for in-plane elastic constants of symmetric damaged laminates

The crack opening and crack sliding displacements of both faces of an intralaminar crack are the main parameters defining the significance of each crack in laminate stiffness degradation, according to the previously published GLOB-LOC approach for symmetric laminates with an arbitrary number of cracks in all plies. In the exact stiffness expressions of this approach, the crack density is always multiplied by crack opening displacement and crack sliding displacement. The dependence of crack opening displacement on geometrical and elastic parameters of adjacent plies was studied previously and described by simple fitting functions. The crack sliding displacement has been analyzed for low-crack densities only and the proposed finite element method-based fitting expressions are oversimplified not including the out-of-plane ply stiffness effects. Based on finite element method analysis, more accurate expressions for so-called non-interactive cracks are suggested in the presented article. For the first time the shear stress perturbations are analyzed and interaction functions are presented with the feature that they always lead to slightly conservative predictions. The presented simple fitting functions, when used in the GLOB-LOC model, give predictions that are in a good agreement with finite element method results and with experimental data for laminates with damaged off-axis plies in cases when crack face sliding is of importance. The significance of including crack sliding displacement in stiffness predictions is demonstrated.

Physical Fingerprints of the 2O-tαP Phase in Phosphorene Stacking.

The 2O-tαP phase is a bilayer phosphorene stacking twisted by ∼70.5° standing out from all the potential candidates predicted by our previous work. Here, by linear response theory, we directly verified that the 2O-tαP phase preserves the intrinsic features of phonon spectrum of the existing AB phase, reflecting a stable thermodynamic behavior. Then we provided three distinct fingerprints to help finding this new phase: upon comparison to the existing shifting bilayer phosphorene, the in-plane elastic constants showed a much weaker anisotropic response, providing a characteristic mechanical criterion; the calculated Raman spectrum revealed forthe low frequency rang thelayer-breathing modeand theout-of-plane twisted mode, L-A1 and L-A2, both of which together stabilize the twisted structure; in particular, thesimulated scanning tunneling microscope image presented recognizable cross stripes, which should withstand an examination of exfoliated bilayer and few-layer black phosphorus.