Linear Elastic Regime Research Articles

Linear aeroelastic analysis of cantilever hybrid composite laminated plates with curvilinear fibres and carbon nanotubes

In this paper, cantilever laminated composite plates, subjected to supersonic airflow, are studied in the linear elastic regime. The considered material is a multiscale three-phase composite, constituted by epoxy resin reinforced with multi-walled carbon nanotubes and curvilinear carbon fibres. The orientation of the fibres is defined using three different functions. A model based on a third-order shear deformation theory and a p-version finite element is applied. Furthermore, a hierarchical approach is applied to characterise the mechanical properties of the composite material. A combination of adequate micromechanics based models, including a modified version of the Halpin-Tsai model, the Rule of Mixtures, a unit cell-based model, and the Chamis model, is implemented. The aeroelastic analysis is performed considering the linear piston theory to evaluate flutter (dynamic instability) and divergence (static instability) in such structures. The improvements achieved through the combination of carbon nanotubes and curvilinear fibres on the instabilities are explored.

How spiders hunt heavy prey: the tangle web as a pulley and spider's lifting mechanics observed and quantified in the laboratory.

The spiders of Theridiidae's family display a peculiar behaviour when they hunt extremely large prey. They lift the quarry, making it unable to escape, by attaching pre-tensioned silk threads to it. In this work, we analysed for the first time in the laboratory the lifting hunting mechanism and, in order to quantify the phenomenon, we applied the lifting mechanics theory. The comparison between the experiments and the theory suggests that, during the process, spiders do not stretch the silk too much by keeping it in the linear elastic regime. We thus report here further evidence for the strong role of silk in spiders' evolution, especially how spiders can stretch and use it as an external tool to overcome their muscles' limits and capture prey with large mass, e.g. 50 times the spider's mass.

Simulated mechanical properties of finite-size graphene nanoribbons

There are many simulation studies of mechanical properties of graphene nanoribbons (GNR), but there is a lack of agreement regarding elastic and plastic behavior. In this paper we aim to analyze mechanical properties of finite-size GNR, including elastic modulus and fracture, as a function of ribbon size. We present classical molecular dynamics simulations for three different empirical potentials which are often used for graphene simulations: AIREBO, REBO-scr and REAXFF. Ribbons with and without H-passivation at the borders are considered, and the effects of strain rate and different boundaries are also explored. We focus on zig-zag GNR, but also include some armchair GNR examples. Results are strongly dependent on the empirical potential employed. Elastic modulus under uniaxial tension can depend on ribbon size, unlike predictions from continuum-scale models and from some atomistic simulations, and fracture strain and progress vary significantly amongst the simulated potentials. Because of that, we have also carried out quasi-static ab-initio simulations for a selected size, and find that the fracture process is not sudden, instead the wave function changes from Blöch states to a strong interaction between localized waves, which decreases continuously with distance. All potentials show good agreement with DFT in the linear elastic regime, but only the REBO-scr potential shows reasonable agreement with DFT both in the nonlinear elastic and fracture regimes. This would allow more reliable simulations of GNRs and GNR-based nanostructures, to help interpreting experimental results and for future technological applications.

Exact axisymmetric adhesive contact analysis for a pre-deformed soft electroactive half-space

In this paper, three-dimensional exact solutions of adhesive contact between a pre-deformed compressible soft electroactive half-space and an axisymmetric rigid indenter are presented. The change of surface adhesion energy during the contact is examined by using the modified JKR model, which accounts for the real contact area instead of the projected area. With the help of new results in the potential theory method, all physical (field) variables are derived in terms of elementary functions for three common types of axisymmetric indenters (flat-ended, conical, and spherical). The analytical contact relations for different indenter geometries and material properties are provided and summarized in Tables 2 and 3 to serve a solid base for revealing the underlying electromechanical mechanism of soft electroactive materials. For numerical illustration, neo-Hookean isotropic electroactive material is considered. The simulation results clearly demonstrate that both the mechanical and electric biasing fields significantly affect the indentation measurement of the electroactive material. Moreover, at either micro- or nano-scale, adhesion plays a prominent role in the indentation responses. It is of interest that, even without adhesion, the normal stress somewhere in the contact region may become tensile under a prescribed pre-stretch when the biasing electric displacement exceeds a certain value. This abnormal phenomenon actually corresponds to surface instability of the half-space under the biasing field. In the case of adhesive contact, other than the surface instability, the value of surface adhesion energy between the probe and the sample will impose a constraint on the validity of indentation analysis within the linear elastic regime.

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

In this work, Discrete Elements Method simulations are carried out to investigate the effective stiffness of an assembly of frictional, elastic spheres under anisotropic loading. Strain probes, following both forward and backward paths, are performed at several anisotropic levels and the corresponding stress is measured. For very small strain perturbations, we retrieve the linear elastic regime where the same response is measured when incremental loading and unloading are applied. Differently, for a greater magnitude of the incremental strain a different stress is measured, depending on the direction of the perturbation. In the case of unloading probes, the behavior stays elastic until non-linearity is reached.Under forward perturbations, the aggregate shows an intermediate inelastic stiffness, in which the main contribution comes from the normal contact forces. That is, when forward incremental probes are applied the behavior of anisotropic aggregates is an incremental frictionless behavior. In this regime we show that contacts roll or slide so the incremental tangential contact forces are zero.Graphical

Estimation of the hyperelastic parameters of fresh human oropharyngeal soft tissues using indentation testing

Patient-specific finite element (FE) modeling of the upper airway is an effective tool for accurate assessment of obstructive sleep apnea (OSA) syndrome. It is also useful for planning minimally invasive surgical procedures under severe OSA conditions. A major requirement of FE modeling is having reliable data characterizing the biomechanical properties of the upper airway tissues, particularly oropharyngeal soft tissue. While some data characterizing this tissue's linear elastic regime is available, reliable data characterizing its hyperelasticity is scarce. The aim of the current study is to estimate the hyperelastic mechanical properties of the oropharyngeal soft tissues, including the palatine tonsil, soft palate, uvula, and tongue base. Fresh tissue specimens of human oropharyngeal tissue were acquired from 13 OSA patients who underwent standard surgical procedures. Indentation testing was performed on the specimens to obtain their force–displacement data. To determine the specimens' hyperelastic parameters using these data, an inverse FE framework was utilized. In this work, the hyperelastic parameters corresponding to the commonly used Yeoh and 2nd order Ogden models were obtained. Both models captured the experimental force-displacement data of the tissue specimens reasonably accurately with mean errors of 11.65% or smaller. This study has provided estimates of the hyperelastic parameters of all upper airway soft tissues using fresh human tissue specimens for the first time.

Study on the Mechanical Properties of Coal Weakenedby Acidic and Alkaline Solutions

A novel method for fracturing coal is presented in this paper. A chemical solution is injected into coal under high pressure, whereby the coal is fractured and subsequently weakened by chemical erosion over time to produce an anti‐impact soft structure. In this study, the mechanical properties of coal under chemical erosion were investigated, and the fracturing design parameters were optimized. The uniaxial compression test and the split Hopkinson pressure bar (SHPB) test were used to determine the dynamic and static mechanical properties of coal after 20 days of immersion in different chemical solutions. After chemical solution erosion, the dynamic and static compressive strengths and elastic modulus of the coal decreased according to an exponential power law in the damage variable. The chemical treatment increased the duration of the pore compaction stage and decreased that of the elastic deformation stage, while decreasing the brittleness and increasing the ductility of coal. The acoustic emission (AE) curve of the immersed coal samples consisted of four stages corresponding to those of the stress‐strain curve: pore compaction‐closure, a slowly rising linear elastic regime, steady‐state prepeak crack propagation, and unsteady crack propagation at the peak strain. The increase in the damage variable of the coal sample from chemical erosion led to a lower dissipated energy, a higher fractal dimension, and a more fragmented coal sample. The effect of the investigated chemical solutions on weakening the coal mechanical properties decreased in the following order: alkaline solution > acidic solution > NaCl solution > distilled water. The experimental results provide a reference for weakening fractured coal seams.

Stability, elastic properties and deformation behavior of graphene-based diamond-like phases

Abstract The stability, elastic moduli and deformation behavior of graphene-based diamond-like phases are examined by molecular dynamics simulations. Three important criteria are considered to study stability of the structure within applied methods. Molecular dynamics simulations are performed to derive stiffness and compliance coefficients, and stress-strain curves under hydrostatic compression of diamond-like phases. The analysis of elastic properties (Poisson’s ratio, Young’s modulus and shear modulus) is carried out. Analytical calculations are used. From the obtained stability criteria, it is found that only two graphene-based diamond-like phases, LA3 and LA6, instead of eight known, can be considered stable in molecular dynamics approach. Young’s modulus, measured in linear elastic regime, of stable phases orientationally dependent: values in different directions can differ two times. Analysis of the variability of shear modulus showed that for LA6 values are much higher than for LA3. Again, shear modulus are orientation-dependent for some directions. In non-elastic regime, stable diamond-like phases can be stretched until 0.012 and compressed until 0.1. The main mechanisms of non-elastic deformation is stretching of the covalent bonds and valent angles.

Failure analysis of a sugarcane loader rear shaft

This work deals with the failure analysis of rear differential shaft of a sugarcane loader that broke in less than a year of use. For the analysis of fracture, fracture surface macrographs, microhardness profile and metallographic analysis were realized. It was also carried out a numerical simulation of shaft estimating the external stresses applied during use. The numerical simulation was performed in linear elastic regime. The microstructure on the surface is composed of martensite and ferrite caused by the superficial hardening heat treatment and in the core formed by perlite and ferrite. The microhardness profile showed a hardness peak of 648 HV in the peripheral region of the shaft. From the analysis of the fracture surface it was possible to observe that the failure occurred in unidirectional fatigue of high cycle, and we observed several ratchet marks along the rounding radius of the shaft. The numerical simulation permitted to quantify the stresses and showed that rounding radius in the shaft base was the cause of failure.

Determination of the linear elastic regime in AFM nanoindentation experiments on cells

Atomic force microscopy nanoindentation method has been extensively used for the determination of cells’ mechanical properties. The data processing is usually performed using contact mechanics models at the linear elastic regime such as the Hertz model. It should be noted that the cells’ response can be considered as linearly elastic only for a limited range of indentation depths. Although there are in literature proposed values of the maximum allowed nanoindentation depth for most of the cell types, these values have been mostly derived empirically. As a result, the use of these empirically obtained findings can result in significant errors regarding Young’s modulus calculations. A large number of measurements, using spherical and conical indenters, showed errors in the range of 4−10% with respect to the Young’s modulus calculation. In this paper, a new mathematical approach is proposed that enables the identification of the optimum load - indentation data range for the application of the Hertz contact theory. The results presented in this paper indicate that the optimum choice of the maximum indentation depth can vary greatly even in the same sample. For example, 64 load indentation curves on the same cell using a spherical indenter showed that the maximum indentation depth is (553 ± 43)nm (mean value ± standard deviation). As a consequence, the determination of a specific maximum indentation depth for indentation experiments on a specific cell will lead to significant errors regarding Young’s modulus values. Hence, the selection of the linear elastic regime must be performed individually for each load—indentation curve to accurately determine the cell’s mechanical response.

Primary and secondary pyroelectric effects in macro-fiber composites

Materials like the Macro-fiber Composite (MFC) are employed in energy harvesting applications utilizing the piezoelectric effect. However, energy harvesting using the pyroelectric effect in MFCs is an unexplored topic. This paper takes strides in understanding the thermal micromechanical interactions that MFCs experience due to this effect and leads to a better understanding of how MFCs behave in thermal environments. In this work, the pyroelectric coefficient (primary and secondary) are estimated for P1 and P2 Macro-fiber Composites (MFCs) using micromechanical modeling and experimental techniques. The coefficient of thermal expansion (CTE) is estimated using micromechanical theory for both MFC types which is consequently used in the modeling of the pyroelectric coefficient. Secant based moduli are used to better approximate the properties of components of MFCs in the regime of linear elasticity. Two experiments are conducted to measure the pyroelectric coefficient under different boundary conditions. In the first experiment, the thermal expansion of the MFC is constrained in a Kevlar envelope, while in the second experiment, the MFC is epoxied onto a metal shim allowing restricted deformations. Thermal experiments were conducted in an altitude chamber where the resulting average pyroelectric coefficient is calculated for both experiments.

Strain in Lattice-Mismatched CdSe-Based Core/Shell Nanoplatelets

We investigate the role of stress arising between core and shell materials in colloidal CdSe/X hetero-nanoplatelets (X = ZnS, CdS, CdTe). The resulting strain distribution is calculated within the linear elastic regime and also its influence on the electronic structure with k·p theory. We show that strain shifts the energy of electrons and that of holes by several tens of megaelectronvolts (meV). In structures with type I band alignment, the two shifts have opposite signs and the net effect on the exciton emission energy is small, but both these add up in type II systems. The strain response in colloidal nanoplatelets (NPLs) is found to exhibit some differences as compared to that of epitaxial quantum wells, including a sizable influence of lateral dimensions below 10 nm and a potentially relevant effect of coupled strain–momentum terms of the Hamiltonian. We further show that an asymmetric shell covering leads to bending of the nanoplatelet and tilted potential profiles along the strong confinement direc...

Revisiting the Dependence of Poisson's Ratio on Liquid Fragility and Atomic Packing Density in Oxide Glasses.

Poisson’s ratio (ν) defines a material’s propensity to laterally expand upon compression, or laterally shrink upon tension for non-auxetic materials. This fundamental metric has traditionally, in some fields, been assumed to be a material-independent constant, but it is clear that it varies with composition across glasses, ceramics, metals, and polymers. The intrinsically elastic metric has also been suggested to control a range of properties, even beyond the linear-elastic regime. Notably, metallic glasses show a striking brittle-to-ductile (BTD) transition for ν-values above ~0.32. The BTD transition has also been suggested to be valid for oxide glasses, but, unfortunately, direct prediction of Poisson’s ratio from chemical composition remains challenging. With the long-term goal to discover such high-ν oxide glasses, we here revisit whether previously proposed relationships between Poisson’s ratio and liquid fragility (m) and atomic packing density (Cg) hold for oxide glasses, since this would enable m and Cg to be used as surrogates for ν. To do so, we have performed an extensive literature review and synthesized new oxide glasses within the zinc borate and aluminoborate families that are found to exhibit high Poisson’s ratio values up to ~0.34. We are not able to unequivocally confirm the universality of the Novikov-Sokolov correlation between ν and m and that between ν and Cg for oxide glass-formers, nor for the organic, ionic, chalcogenide, halogenide, or metallic glasses. Despite significant scatter, we do, however, observe an overall increase in ν with increasing m and Cg, but it is clear that additional structural details besides m or Cg are needed to predict and understand the composition dependence of Poisson’s ratio. Finally, we also infer from literature data that, in addition to high ν, high Young’s modulus is also needed to obtain glasses with high fracture toughness.

Continuum stress intensity factors from atomistic fracture simulations

Stress intensity factors (SIFs) are used in continuum fracture mechanics to quantify the stress fields surrounding a crack in a homogeneous material in the linear elastic regime. Critical values of the SIFs define an intrinsic measure of the resistance of a material to propagate a crack. At atomic scales, however, fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analog of the continuum SIFs calculated from atomistic simulations can have spatially localized, microstructural contributions that originate from varying bond configurations. The ability to characterize fracture at the atomic scale in terms of the SIFs offers both an opportunity to probe the effects of chemistry, as well as how the addition of a microstructural component affects the accuracy. We present a novel numerical method to determine SIFs from molecular dynamics (MD) simulations. The accuracy of this approach is first examined for a simple model, and then applied to atomistic simulations of fracture in amorphous silica. MD simulations provide time and spatially dependent SIFs, with results that are shown to be in good agreement with experimental values for fracture toughness in silica glass.

Rheological Characterization of Next-Generation Ballistic Witness Materials for Body Armor Testing.

Roma Plastilina No. 1 (RP1), an artist modeling clay that has been used as a ballistic clay, is essential for evaluation and certification in standards-based ballistic resistance testing of body armor. It serves as a ballistic witness material (BWM) behind the armor, where the magnitude of the plastic deformation in the clay after a ballistic impact is the figure of merit (known as “backface signature”). RP1 is known to exhibit complex thermomechanical behavior that requires temperature conditioning and frequent performance-based evaluations to verify that its deformation response satisfies requirements. A less complex BWM formulation that allows for room-temperature storage and use as well as a more consistent thermomechanical behavior than RP1 is desired, but a validation based only on ballistic performance would be extensive and expensive to accommodate the different ballistic threats. A framework of lab-scale metrologies for measuring the effects of strain, strain rate, and temperature dependence on mechanical properties are needed to guide BWM development. The current work deals with rheological characterization of a candidate BWM, i.e., silicone composite backing material (SCBM), to understand the fundamental structure–property relationships in comparison to those of RP1. Small-amplitude oscillatory shear frequency sweep experiments were performed at temperatures that ranged from 20 °C to 50 °C to map elastic and damping contributions in the linear elastic regime. Large amplitude oscillatory shear (LAOS) experiments were conducted in the non-linear region and the material response was analyzed in the form of Lissajous curve representations with the values of perfect plastic dissipation ratio reported to identify the degree of plasticity. The results show that the SCBM exhibits dynamic properties that are similar in magnitude to those of temperature-conditioned RP1, but with minimal temperature sensitivity and weaker frequency dependence than RP1. Both SCBM and RP1 are identified as elastoviscoplastic materials, which is particularly important for accurate determination of backface signature in body armor evaluation. The mechanical properties of SCBM show some degree of aging and work history effects. The results from this work demonstrate that the rheological properties of SCBM, at small and large strains, are similar to RP1 with substantial improvements in BWM performance requirements in terms of temperature sensitivity and thixotropy.

A phase-field formulation for dynamic cohesive fracture

We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress–strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro- and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

Numerical simulation of the hydrogen trapping effect on crack propagation in API 5CT P110 steel under cathodic overprotection

The possibility of the development of hydrogen embrittlement processes increases in cathodic protection systems when cathodic overprotection occurs, and large amounts of hydrogen are produced. Additionally, the hydrogen embrittlement susceptibility of steel depends on solubility, diffusivity, and hydrogen trapping. This paper presents a numerical simulation of the reversible and irreversible hydrogen trapping effects on crack propagation in API 5CT P110 steel using a model based on a synthesis of fracture mechanics and continuum damage mechanics, in which the trapping term of the diffusion equation was replaced by the trapping terms of other more complete model. The simulation was performed with using a C(T) specimen loaded in the tensile opening mode, in the linear elastic regime, in plane strain state, under the action of a static mechanical loading and the effect of hydrogen. The simulations showed that the material degradation ahead of the crack tip increases with increases in hydrogen concentration at the crack tip due to the hydrogen trapping effect. Furthermore, the process of onset and crack growth in material with irreversible traps is slower than that in material with reversible traps. These results are consistent with macroscopic observations of the trapping effect, providing a better understanding of the hydrogen embrittlement in structural steels.

Adaptive locally resonant metamaterials leveraging shape memory alloys

Locally resonant metamaterials leveraging shape memory alloy (SMA) springs are explored in this work in an effort to develop adaptive metamaterial configurations that can exhibit tunable bandgap properties as well as enhanced damping capabilities. An analytical model for a locally resonant metamaterial beam in transverse vibrations is combined with an SMA model for the resonator springs to investigate and leverage the potential of temperature-induced phase transformations and stress-induced hysteretic behavior of the springs. Two case studies are presented for this new class of smart metamaterials and the resulting finite metastructures. In one case, SMA resonators operate in the linear elastic regime, first at low temperature (martensitic behavior) and then at high temperature (austenitic behavior), demonstrating how the bandgap can be tuned to a different frequency range by altering the SMA elastic modulus with temperature. In the second case, the SMA springs are kept at high temperature at all times to operate in the nonlinear regime, so that the hysteresis associated with the SMA pseudoelastic effect is manifested, yielding additional dissipation over a range of frequencies, especially for the modes right outside the bandgap.

Strain and damage-sensing performance of biocompatible smart CNT/UHMWPE nanocomposites

Herein, we report strain- and damage-sensing performance of biocompatible smart CNT/UHMWPE nanocomposites for the first time. CNT/UHMWPE nanocomposites are fabricated by solution mixing followed by compression molding. The surface morphology, microstructural properties, thermal decomposition and stability, glass transition temperature and thermal conductivity of the nanocomposites are characterized. The degree of crystallinity of CNT/UHMWPE nanocomposites is found to have a maximum value of 52% at 0.1 wt% CNT loading. The degree of crystallinity influences the mechanical properties of the CNT/UHMWPE nanocomposites. The electrical percolation threshold is achieved at 0.05 wt% of CNT and it follows a two dimensional conductive network according to percolation theory. The piezoresistive response of CNT/UHMWPE nanocomposites is demonstrated with a gauge factor of ~2.0 in linear elastic regime and that in the range of 3.8–96.0 in inelastic regimes for 0.05 wt% of CNT loading. A simple theoretical model is also developed to predict the resistivity evolution in both elastic and inelastic regimes. High sensitivity of CNT/UHMWPE nanocomposites coupled with linear piezoresistive response up to 100% strain demonstrates their potential for application in artificial implants as a self-sensing material.

Estimation of the Young's moduli of fresh human oropharyngeal soft tissues using indentation testing.

Finite element (FE)-based biomechanical simulations of the upper airway are promising computational tools to study abnormal upper airway deformations under obstructive sleep apnea (OSA) conditions and to help guide minimally invasive surgical interventions in case of upper airway collapse. To this end, passive biomechanical properties of the upper airway tissues, especially oropharyngeal soft tissues, are indispensable. This research aimed at characterizing the linear elastic mechanical properties of the oropharyngeal soft tissues including palatine tonsil, soft palate, uvula, and tongue base. For this purpose, precise indentation experiments were conducted on freshly harvested human tissue samples accompanied by FE-based inversion schemes. To minimize the impact of the probable nonlinearities of the tested tissue samples, only the first quarter of the measured force-displacement data corresponding to the linear elastic regime was utilized in the FE-based inversion scheme to improve the accuracy of the tissue samples' Young's modulus calculations. Measured Young's moduli of the oropharyngeal soft tissues obtained in this study are presented. They include first estimates for palatine tonsil tissue samples while measured Young's moduli of other upper airway tissues were obtained for the first time using fresh human tissue samples.