In-plane Elasticity Research Articles

Superior bendability enabled by inherent in-plane elasticity in Bi2Te3 thermoelectrics

With the rapid development of modern wearable electronics, powerful and deformable thermoelectric generators have become an urgent need as the power units that convert environmental or body heat into electricity. Existing efforts mostly focused on the assistance for deformability by substrates/additives, the resultant devices usually output much less power and showed very poor power retainment. Elasticity is inherent to all solids, which therefore offers an intrinsic solution for making thermoelectrics deformable without compromise in power output because of its full recoverability. This work demonstrates this in best-performing (Bi, Sb)2(Te, Se)3 thermoelectrics near room temperature, ending up in the film devices with both extraordinary power density and robust recoverable bendability. This originates from the inherent large elasticity for the in-plane orientation, which is enabled by an easy tape stripping approach for the Van der Waals layered structure, allowing the realization of both powerfulness and bendability that are equally important for wearable thermoelectrics.

Mesoscale modeling of deformations and defects in thin crystalline sheets

We present a mesoscale description of deformations and defects in thin, flexible sheets with crystalline order, tackling the interplay between in-plane elasticity, out-of-plane deformation, as well as dislocation nucleation and motion. Our approach is based on the Phase-Field Crystal (PFC) model, which describes the microscopic atomic density in crystals at diffusive timescales, naturally encoding elasticity and plasticity effects. In its amplitude expansion (APFC), a coarse-grained description of the mechanical properties of crystals is achieved. We introduce surface PFC and surface APFC models in a convenient height-function formulation encoding deformation in the normal direction. This framework is proven consistent with classical aspects of strain-induced buckling, defect nucleation on deformed surfaces, and out-of-plane relaxation near dislocations. In particular, we benchmark and discuss the results of numerical simulations by looking at the continuum limit for buckling under uniaxial compression and at evidence from microscopic models for deformation at defects and defect arrangements, demonstrating the scale-bridging capabilities of the proposed framework. Results concerning the interplay between lattice distortion at dislocations and out-of-plane deformation are also illustrated by looking at the annihilation of dislocation dipoles and systems hosting many dislocations. With the novel formulation proposed here, and its assessment with established approaches, we envision applications to multiscale investigations of crystalline order on deformable surfaces.

The interplay between membrane viscosity and ligand-binding receptor kinetics in lipid bilayers

Plasma membranes appear as deformable systems wherein molecules are free to move and diffuse giving rise to condensed microdomains (composed of ordered lipids, transmembrane proteins and cholesterol) surrounded by disordered lipid molecules. Such denser and thicker regions, namely lipid rafts, are important communication hubs for cells. Indeed, recent experiments revealed how the most of active signaling proteins co-localize on such domains, thereby intensifying the biochemical trafficking of substances. From a material standpoint, it is reasonable to assume the bilayer as a visco-elastic body accounting for both in-plane fluidity and elasticity. Consequently, lipid rafts contribute to membrane heterogeneity by typically exhibiting higher stiffness and viscosity and by locally altering the bilayer dynamics and proteins activity. A chemo-mechanical model of lipid bilayer coupled with interspecific dynamics among the resident species (typically transmembrane receptors and trasporters) has been recently formulated to explain and predict how proteins regulate the dynamic heterogeneity of membrane. However, the explicit inclusion of the membrane viscosity in the model was not considered. To this aim, the present work enriches the constitutive description of the bilayer by modeling its visco-elastic behavior. This is done through a strain-level dependent viscosity able to theoretically trace back the alteration of membrane fluidity experimentally observed in lipid phase transitions. This provides new insights into how the quasi-solid and fluid components of lipid membrane response interact with the evolution of resident proteins by affecting the activity of raft domains, with effects on cell mechano-signaling.

Interfacial Interactions of a Myoglobin/DOPC Hybrid System at the Air-Water Interface and Its Physicochemical Properties.

In the present study, the intermolecular interactions between a water-insoluble phospholipid (DOPC) and water-soluble protein (myoglobin) and the interaction among themselves were investigated at the air-water interface using the Langmuir and Langmuir-Blodgett techniques. The effects of changes in physicochemical factors, like pH and temperature, on these interactions were also examined. Surface pressure-molecular area (π-A) isotherms of the DOPC monolayer at the air-water interface, with and without myoglobin (Myo) revealed the evolution of various physical properties, such as elastic, thermodynamic, and hysteric properties, in response to changes in subphase pH and temperature. With the increment of subphase pH from 5 to 7 at a fixed temperature (20 °C), the DOPC isotherm expanded, and the in-plane elasticity (CS-1) decreased, but no significant presence of hysteresis was encountered in either of the pH values. On the other hand, a diminution of temperature (from 20 to 5 °C) leads to an expansion of monolayers yielding low elasticity and significant hysteresis. The incorporation of Myo molecules within the DOPC monolayer decreased the CS-1 value of the DOPC monolayer. Such a decrement in CS-1 was also encountered while increasing the pH and decreasing the temperature (T) of the subphase in the absence of Myo. Systematic expansion of DOPC isotherm and increased hysteric area with the increase in Myo proportion were observed and the atomic force microscopy (AFM) observations suggested a strong conjugation between Myo and DOPC in the mixed monolayer. The denaturation effect of Myo molecules was studied using AFM at different temperatures. Furthermore, the Myo molecules were found to be most surface active at pH = 7, which is very close to its isoelectric point. These observations come up with the interaction mechanism between biomolecules under dynamically varied conditions.

Symplectic superposition solutions for free in-plane vibration of orthotropic rectangular plates with general boundary conditions

This work reports new analytic free in-plane vibration solutions for orthotropic non-Lévy-type rectangular plates, i.e., those without two opposite edges simply supported, by the symplectic superposition method (SSM), which has never been applied to in-plane elasticity problems in any existing works. Such analytic solutions are not accessible through conventional analytic methods as seeking analytic solutions that meet both the governing partial differential equations and various non-Lévy-type boundary conditions is an acknowledged challenge in mechanical analysis of plates. The clamped and free plates are considered as two most representative cases of non-Lévy-type plates. The SSM is implemented in the Hamiltonian system-based symplectic space, where the separation of variables and the symplectic eigen expansion prove to be well-grounded. These two mathematical treatments are adopted to first gain the analytic solutions of two elementary problems. The final analytic free in-plane vibration solutions are obtained by superposition of the two elementary problems. Comprehensive new natural frequencies and vibration modes are studied and validated by reference solutions from the finite element method or other approaches. The rigorous solution procedure, fast convergence, and highly accurate results render the present framework capable of serving as benchmarks for future comparison and applicable to analytic investigation of more plate problems.

The composition of fusogenic lipid mixtures at the air-water modulates the physicochemical properties changes upon interaction with lysicamine

Knowing how a bioactive compound interacts with cell membranes is important to understand its effect at the molecular level. In this sense, this work aimed to study the interaction of lysicamine, an alkaloid with action against lung cancer cell lines, with lipid monolayers as cell membrane models. We employed two lipid mixtures: the first composed of 35% DOPC, 30% DOPE, 20% sphingomyelin, and 15% cholesterol as healthy cell membranes models (MM1), and the second replacing DOPC with DOPS as cancer cells models (MM2). The interaction of lysicamine with the monolayers was evaluated using tensiometry, Brewster angle microscopy (BAM), and polarization-modulated infrared reflection-absorption spectroscopy (PM-IRRAS). Lysicamine had interfacial effects in both membrane models. For MM 1, it expanded the lipid monolayer and changed the interfacial rheological properties, increasing the in-plane elasticity of the films. PM-IRRAS spectra suggested a higher conformational disorder of the alkyl chains of the lipids. For MM 2, lysicamine also shifted the isotherms to higher areas, expanding the monolayers, but with no significant alteration in their interfacial rheological properties. PM-IRRAS spectra also suggested higher disorder in the orientation of the lipid alkyl chains upon lysicamine incorporation. For both models, BAM did not show alteration in interfacial aggregation upon drug incorporation. In conclusion, changes in some interfacial properties of membrane models caused by lysicamine depend on the monolayer composition, which can be associated with its bioactivity in cellular membranes.

Nanoscale mechanism of suppression of friction and wear of the diamond substrate by graphene

Reducing friction and wear are critical for improving the properties of diamond-based devices. Especially in the field of micro/nano-electro-mechanical systems (MEMS/NEMS) and ultra-precision machining (UPM). Friction and wear have more serious impacts on material performance owing to size effects. In this study, the graphene/diamond interfacial structure was created to improve the mechanical properties of the diamond substrate. The properties of suppression of friction and wear of the diamond substrate by graphene were investigated using molecular dynamics simulations. It was found that graphene effectively suppressed the friction and wear of the diamond, reducing the occurrence of surface scratches and subsurface amorphisation. The suppression effect was more evident as the number of graphene layers increased. In addition, the mechanism of suppression of graphene was revealed based on graphene wrinkles, system energy, contact interface properties and atomic stress. The simulation results showed that graphene modified the contact pattern between the indenter and the diamond substrate, which suppressed the efficiency of energy dissipation. The in-plane elasticity of graphene absorbed part of the external load and enhanced the load-bearing capacity. The atomic stress peaks of the diamond were reduced, and the atomic stress distribution was more homogenous due to the protection of graphene. This investigation will provide theoretical support for applying graphene as a lubricating medium in diamond-based devices.

Pre-buckling vibration and buckling analyses of composite skew plate: An analytical investigation

In this work, the analytical investigation for pre-buckling vibration and buckling analyses of a composite skew plate subjected to parabolically and linearly varying in-plane edge load are presented. When the composite skew plate is subjected to parabolic (non-uniform) in-plane edge loading, the pre-buckling stresses within the composite skew plate are not known a priori. To estimate the pre-buckling stresses within the composite skew plate for which the in-plane elasticity problem is solved by minimizing the membrane strain energy using the Ritz method. It is observed that the rate of diffusion of applied parabolic in-plane edge load within the skew plate to a state of uniform in-plane stress is faster in the case of isotropic material than composite material. Using estimated pre-buckling stresses, the total energy functional is derived from the total strain energy, potential energy, and kinetic energy. The total energy functional is reduced into sets of an ordinary differential equation and algebraic equation, respectively for pre-buckling vibration and buckling problems using the Ritz method in conjunction with BCOPs. The associated linear eigenvalue problems are solved to compute the pre-buckling vibration frequency and buckling load of the stressed skew plate. The outcome of the study may provide crucial inputs in the design of skewed bridge decks, ship structures, and aircraft wing design.

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.

In-plane elasticity of a novel arcwall-based double-arrowed auxetic honeycomb design: Energy-based theoretical analysis and simulation

In this paper, a new design of auxetic honeycomb is proposed for mechanical performance enhancement by combining the arc-shaped wall and the normal double-arrowed auxetic configuration. On basis of Mohr's 2nd theorem and Castigliano 2nd theorem, an analytical model considering strut bending and stretching is developed to modulate the in-plane mechanical properties of the proposed honeycomb with the geometric parameters. Further, an integrated experimental, simulation and theoretical approach is carried out to investigate its elastic properties and Poisson's ratios in a wide range. The comparison shows that the theoretical results are in good agreement with the experimental and simulation results, verifying the established analytical model. The results reveal that both the in-plane modulus and the Poisson's ratio of the proposed auxetic honeycomb are simultaneously improved compared to the typical double-arrowed and the re-entrant hexagonal designs, and show high and diverse dependencies on the geometric parameters. Additionally, the honeycomb features a stiffer modulus and stronger auxeticity along y direction than that along x direction when the arc angle of “bone”, θ1, not exceeding a “turning point”. The present design may provide an extensive reference for the design and application of mechanical meta-materials.

Mechanical performance of 3D-printing annular honeycomb with tailorable Poisson’s ratio

This paper reports a new annular honeycomb that shows tunable Poisson’s ratio. The presented honeycombs can provide both the in-plane negative Poisson’s ratio (NPR) and in-plane zero Poisson’s ratio (ZPR) while the shapes of the honeycomb core change. The developed honeycomb core is constructed by an annulus with four ligaments distributed bi-axial symmetrically, which shows great diversity of mechanical properties. The developed theoretical models of the in-plane elasticity are based on Castigliano’s Second Theorem and energy principle. Two parameters were used to describe the deformation mechanisms of the unit cell concisely. The effect of two parameters on the Poisson’s ratio and Young’s modulus was investigated. The Young’s modulus derived from the Finite Element (FE) analysis all have an good agreement with that derived from theoretical results, and the experiments were carried out to confirm the validity of them convincingly.

Physicochemical Properties of a Bi-aromatic Heterocyclic-Azo/BSA Hybrid System at the Air-Water Interface.

The interaction of a heterocyclic azo compound with itself and with bovine serum albumin (BSA) is realized by probing the structural modifications in Langmuir (L) monolayers and Langmuir–Blodgett (LB) films. It was found from the pressure–area/molecule isotherms that the elastic, thermodynamic, and hysteretic properties of the pure azo L monolayer were strongly altered due to the variation of temperature and pH of subphase water. In addition to that, the modification of such properties of the azo L monolayer due to mixing with BSA was also studied. The incorporation of BSA within the azo molecular assembly reduced the elasticity of that assembly. Such reduction of in-plane elasticity of the pure azo monolayer can also be achieved by reducing the temperature and pH of subphase water without adding BSA. A reduction in area per molecule of the azo assembly at the air–water interface associated with the conformational change from horizontal to vertical orientation facilitating π–π interaction was observed with increase in temperature and pH of the subphase. Such parameters also affected the interactions between azo and BSA molecules within the azo/BSA binary system. The structures of pure azo and binary films can be determined after they are transferred to hydrophilic and hydrophobic Si surfaces using the LB technique. Their out-of-plane and in-plane structures, as extracted from two complementary surface sensitive techniques, X-ray reflectivity and atomic force microscopy, were found to be strongly dependent on mixing with BSA, subphase pH, temperature, and substrate nature.

Interface mechanics of 2D materials on metal substrates

The chemical vapor deposition (CVD) of graphene on metal substrate serves as a robust method to synthesize large graphene flakes. Therefore, understanding the thermodynamics and kinetics of graphene–metal interface is an important step towards synthesizing defect-free graphene during CVD. The focus of this paper is on the phenomenon of surface reconstruction of a metal substrate during the deposition of a 2D material. Key features of surface reconstruction include the formation of straight and pyramidal facets of size ∼300 nm in width and ∼15–80 nm in height. In addition, discontinuities in facet directions under a single graphene flake distributed over two grains highlight the strong crystallographic influence on surface reconstruction.In this paper, we present an atomistically informed continuum model of a graphene–metal interface in three dimensions. Graphene is modeled as an elastic surface that is in contact with a rigid metal substrate. Due to the weak van der Waals interaction between graphene and metal, the kinematics of the model incorporates sliding of graphene. However, since we assume that graphene is always in contact with the substrate, its normal displacement is mediated by surface diffusion of metal atoms. Based on evidence from recent molecular dynamics simulations and experiments, we model the graphene-covered-metal surface energy to include in-plane elasticity and bending energy of graphene, and an interaction energy that depends on the orientation of graphene relative to the substrate. We compare the predictions of our model with surface reconstructions observed during the CVD of graphene on forged thin film palladium polycrystals. As we continue to unravel the atomic scale mechanisms responsible for surface reconstruction during CVD, we expect the current continuum framework and its generalizations will serve to bridge the atomic- and the meso-scales.

In-plane elasticity of the re-entrant auxetic hexagonal honeycomb with hollow-circle joint

This work proposed an improved modification on the common re-entrant hexagonal honeycomb (RHH) by replacing the solid junction of the cell walls with a small hollow circle, and thus achieving a novel kind of honeycomb. A simple energy-based approach was adopted to develop theoretical models for predicting the in-plane equivalent elastic moduli of the new honeycomb. Finite element analysis was employed to verify the theoretical models and then the effects of the micro geometrical parameters on the in-plane elastic behaviors were further discussed. The results showed that the new honeycomb possesses an obvious negative Poisson's ratio effect, meanwhile, can achieve higher specific Young's modulus and shear modulus than the RHH. Moreover, the new honeycomb was found to exhibit a more tailored anisotropy than the RHH from the off-axial properties analysis. As a result, the new honeycomb may be an effective substitute for the RHH in application and the new layout can be a good guide for the improved design of auxetic honeycombs.

Nonlinear large deformation of a spherical red blood cell induced by ultrasonic standing wave.

A computational model is developed to investigate the nonlinear static deformation of a spherical (osmotically swollen) red blood cell (RBC) induced by ultrasonic standing wave. The ultrasonic standing wave can generate steady acoustic radiation stress to deform the cell, and in turn, the deformed cell reshapes the acoustic field. This is a real-time coupling problem between the acoustic field and the mechanical field. In the computational model, the acoustic radiation stress acting on the RBC membrane is modeled by adopting the nonviscous momentum flux theory. The RBC membrane is modeled as a hyperelastic shell considering the in-plane elasticity, bending elasticity, and surface tension of the membrane. The volume conservation constraint of the membrane sealing fluid is applied to ensure the osmotic balance of the membrane. To address this real-time coupling problem, the computational model is implemented by a finite element method algorithm. The numerical results are compared with the existing theoretical model and experimental data, and the strain hardening trend of the experimental data is successfully predicted, which verifies the accuracy and effectiveness of the computational model. The computational model can accurately extract the mechanical properties of cells from acoustic deformation experiments, which is helpful for the diagnosis of some human diseases.

Lattice relaxation and substrate effects of graphene moiré superlattice

When two two-dimensional (2D) materials with different lattice constants or with different rotation angles are superimposed, a moiré superlattice can be constructed. The electronic properties of the superlattice are strongly dependent on the stacking configuration, twist angle and substrate. For instance, theoretically, when the rotation angle of twisted bilayer graphene is reduced to a set of specific values, the so-called magic angles, flat bands appear near the charge neutrality, and the electron-electron interaction is significantly enhanced. The Mott insulator and unconventional superconductivity are detected in the twisted bilayer graphene with a twist angle around 1.1°. For a moiré pattern with a large enough periodicity, lattice relaxation caused by an interplay between van der Waals force and the in-plane elasticity force comes into being. The atomic relaxation forces atoms to deviate from their equilibrium positions, and thus making the system reconstructed. This review mainly focuses on the effects of the lattice relaxation and substrates on the electronic properties of the graphene superlattices. From both theoretical and experimental point of view, the lattice relaxation effects on the atomic structure and electronic properties of graphene-based superlattices, for example, the twisted bilayer graphene, twisted trilayer graphene, graphene-hexagonal boron nitride superlattice and twisted bilayer graphene-boron nitride superlattice are discussed. Finally, a summary and perspective of the investigation of the 2D material superlattice are presented.

A continuum-molecular model for anisotropic electrically conductive materials

An anisotropic model for two-dimensional electrical conduction, elasticity and fracture is proposed in the peridynamic theoretical framework. Material points interact through elastic non-central pair potentials and inelastic pair potential functions of pairwise elastic and inelastic deformation measure, allowing to obtain a bond-based type model for conductive Cauchy orthotropic media without restrictions in the number of independent material constants. The elasticity of pair interactions can be described mechanistically by equivalent normal and shear springs, whose stiffness varies continuously with the spatial orientation of the ligament and, preserving the elastic symmetries of the material, depends on four material parameters defining in-plane orthotropic classical elasticity. The macroscopic anisotropic conductivity is described instead by continuous functions of the micro-conductive properties of the interparticles interactions. Moreover, non-uniform material toughness is modeled adopting an anisotropic energetic failure criterion related to direction-dependent fracture energy functionals. The accuracy of the proposed model has been assessed by several problems including the anisotropic electrical conduction in multi-phases laminae with a central hole and evolving cracks, and the fracture and damage sensing in cortical bone considering different orientation of the material reference system.

On the role of fibre bonds on the elasticity of low-density papers: a micro-mechanical approach

Fine prediction of the elastic properties of paper materials can now be obtained using sophisticated fibre scale numerical approaches. However, there is still a need, in particular for low-density papers, for simple and compact analytical models that enable the elastic properties of these papers to be estimated from the knowledge of various structural information about their fibres and their fibrous networks. For that purpose, we pursued the analysis carried out in Marulier et al. (Cellulose 22:1517–1539, 2015. https://doi.org/10.1007/s10570-015-0610-6) with low-density papers that were fabricated with planar random and orientated fibrous microstructures and different fibre contents. The fibrous microstructures of these papers were imaged using X-ray synchrotron microtomography. The corresponding 3D images revealed highly connected fibrous networks with small fibre bond areas. Furthermore, the evolutions of their Young’s moduli were non-linear and evolved as power-laws with the fibre content. Current analytical models of the literature do not capture these trends. In light of these experimental data, we developed a fibre network model for the in-plane elasticity of papers in which the main deformation mechanisms of the micromechanical model is the shear of the numerous fibre bonds and their vicinity, whereas the fibre parts far from these zones were considered as rigid bodies. The stiffness tensor of papers was then estimated both numerically using a discrete element code and analytically using additional assumptions. Both approaches nicely fit the experimental trends by adjusting a unique unknown micromechanical parameter, which is the shear stiffness of bonding zones. The estimate of this parameter is relevant in light of several recently reported experimental results.

Interaction of isolinderanolide E obtained from Nectandra oppositifolia with biomembrane models

A long-tail lactone, named isolinderanolide E, was obtained from Nectandra oppositifolia and incorporated in Langmuir monolayers of dipalmitoyl-phosphoethanolamine (DPPE) as a model of microbial membranes. The compound was dissolved in chloroform and mixed with DPPE to provide mixed solutions spread on the air-water interface. After solvent evaporation, mixed monolayers were formed, and surface pressure-area isotherms, dilatational rheology, Brewster angle microscopy (BAM), and infrared spectroscopy were employed to characterize the prodrug-membrane interactions. Isolinderanolide E expanded DPPE monolayers, denoting repulsive interactions. At 30 mN/m, the monolayer presented higher viscoelastic and in-plane elasticity parameters and an increased ratio of all-trans/gauche conformers of the alkyl chains, confirming molecular order. Morphology of the monolayer was analyzed by BAM, which revealed a more homogeneous distribution of Isolinderanolide E along the DPPE monolayer than the prodrug directly spread at the interface, which tends to aggregate. A molecular model proposing the molecular orientation of the amphiphilic drug is presented and explained by the distortion of the alkyl chains as well as by viscoelastic changes. In conclusion, the prodrug changes the thermodynamic, rheological, morphological, and structural properties of the DPPE monolayer, which may be essential to understand, at the molecular level, the action of bioactives in selected membrane models.

Discerning perturbed assembly of lipids in a model membrane in presence of violacein

Violacein is a naturally found pigment that is used by some gram negative bacteria to defend themselves from various gram positive bacteria. As a result, this molecule has caught attention for its potential biomedical applications and has already shown promising outcomes as an antiviral, an antibacterial, and an anti-tumor agent. Understanding the interaction of this molecule with a cellular membrane is an essential step to extend its use in the pharmaceutical paradigm. Here, the interaction of violacein with a lipid monolayer formed at the air–water interface is found to depend on electrostatic nature of lipids. In presence of violacein, the two dimensional (2D) pressure–area isotherms of lipids have exhibited changes in their phase transition pressure and in-plane elasticity. To gain insights into the out-of-plane structural organization of lipids in a membrane, X-ray reflectivity (XRR) study on a solid supported lipid monolayer on a hydrophilic substrate has been performed. It has revealed that the increase in membrane thickness is more pronounced in the zwitterionic and positively charged lipids compared to the negatively charged one. Further, the lipid molecules are observed to decrease their tilt angle made with the normal of lipid membrane along with an alteration in their in-plane ordering. This has been quantified by grazing incidence X-ray diffraction (GIXD) experiments on the multilayer membrane formed in an environment with controlled humidity. The structural reorganization of lipid molecules in presence of violacein can be utilized to provide a detailed mechanism of the interaction of this molecule with cellular membrane.