Effective Young Modulus Research Articles

Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams

Periodic beam networks of Body-Centered Cubic (BCC) symmetry belong to the same family of cubic metamaterials as the well-known Face-Centered Cubic (FCC) octet truss lattice. Analytical closed form expressions are derived to compute their homogenized macroscopic moduli as a function of the relative density. Detailed finite element simulations are performed to confirm the analytical results. The large strain compression response of BCC lattices is also investigated numerically, showing that for any relative density, their crushing response is stable in the sense that the engineering stress-strain curve increases monotonically until densification. Both theoretical considerations and numerical simulations demonstrate that the tapering of the beam cross-sections leads to higher specific mechanical properties, with increases in the effective Young's modulus and specific energy absorption of up to 70% and 45%, respectively. To validate the specific energy absorption estimates, static compression experiments are also performed on specimens of 10%, 20% and 30% relative density and minimum beam diameter of 300 µm made from stainless steel 316 L through selective laser melting. In addition, dynamic compression experiments at strain rates of about 500/s are performed on a Hopkinson pressure bar system revealing a dynamic increase factor of 1.3 for the BCC metamaterials, which is comparable to that of the basis material. The comparison of the BCC and FCC lattice materials shows that the BCC Young's modulus for the stiffest material direction is higher than that for the FCC truss lattice, while the opposite holds true for the softest directions.

Effect of Osmotic Pressure on Cellular Stiffness as Evaluated Through Force Mapping Measurements

Atomic force microscopy (AFM) has been used to measure cellular stiffness at different osmolarities to investigate the effect of osmotic pressure on cells. However, substantial direct evidence is essential to clarify the phenomena derived from the experimental results. This study used both the single-point and force mapping methods to measure the effective Young's modulus of the cell by using temporal and spatial information. The single-point force measurements confirmed the positive correlation between cellular stiffness and osmolarity. The force mapping measurements provided local stiffness on the cellular surface and identified the cytoskeleton distribution underneath the plasma membrane. At hyper-osmolarity, the cytoskeleton was observed to cover most of the area underneath the plasma membrane, and the effective Young's modulus on the area with cytoskeleton support was determined to be higher than that at iso-osmolarity. The overall increase in cellular Young's modulus confirmed the occurrence of cytoskeleton compression at hyper-osmolarity. On the other hand, although the average Young's modulus at hypo-osmolarity was lower than that at iso-osmolarity, we observed that the local Young's modulus measured on the areas with cytoskeleton support remained similar from iso-osmolarity to hypo-osmolarity. The reduction of the average Young's modulus at hypo-osmolarity was attributed to reduced cytoskeleton coverage underneath the plasma membrane.

Piezoelectric properties and Young's moduli of diphenylalanine microtubes—oxide nanoparticles composites

ABSTRACTIn this work, we investigated the influence of piezoelectric ZnO and nonpiezoelectric SiO2 and TiO2 nanoparticles on the structure and some physical properties of composite structures based on microtubes of diphenylalanine. We demonstrated that all types of used nanoparticles promoted formation of voids and cavities in diphenylalanine microtubes thus reducing the effective Young's modulus and lateral piezoelectric coefficient of the composite. At the same time, embedding of piezoelectric ZnO nanoparticles provides noticeable vertical piezoresponse normally absent in single-component diphenylalanine microtubes. The obtained results demonstrate the ability to control the properties of self-assembling composite biomaterials by nanoparticles.

An improved model for predicting effective Young's modulus of the twisted structure under cyclic loading: taking into account the untwisting effect

ABSTRACT Twist structures have diverse applications, ranging from dragline, electrical cable, and intelligent structure. Among these applications, tension deformation can't be avoided during the fabrication and working processes, which often leads to the twist structure rotation (called untwisting effect) and twist pitch increasing. As a consequence, this untwisting behavior has a large effect on the effective Young's modulus. In this paper, we present an improved model based on the classical Costello's theory to predict the effective Young's modulus of the basic structure, twisted by three same copper strands under cyclic loading. Series of experiments were carried out to verify the present model taking into account the untwisting effect. The experimental results have better agreements with the presented model than the common Costello's model.

A continuous crystallographic approach to generate cubic lattices and its effect on relative stiffness of architectured materials

This original work proposes to investigate the transposition of crystallography rules to cubic lattice architectured materials to generate new 3D porous structures. The application of symmetry operations provides a complete and convenient way to configure the lattice architecture with only two parameters. New lattice structures were created by slipping from the conventional Bravais lattice toward non-compact complex structures. The resulting stiffness of the porous materials was thoroughly evaluated for all the combinations of architecture parameters. This exhaustive study revealed attractive structures having high specific stiffness, up to twice as large as the usual octet-truss for a given relative density. It results in a relationship between effective Young modulus and relative density for any lattice structure. It also revealed the opportunity to generate auxetic structures at will, with a controlled Poisson ratio. The collection of the elastic properties for all the cubic structures into 3D maps provides a convenient tool for lattice materials design, for research, and for mechanical engineering. The resulting mechanical properties are highly variable according to architecture, and can be easily tailored for specific applications using the simple yet powerful formalism developed in this work.

Fracture of coherent interfaces between an fcc metal matrix and the Cr23C6 carbide precipitate from first principles

It is known that microcrack initiation in metallic alloys containing second-phase particles may be caused by either an interfacial or an intraprecipitate fracture. So far, the dependence of these features on properties of the precipitate and the interface is not clearly known. The present study aims to determine the key properties of carbide-metal interfaces controlling the energy and critical stress of fracture, based on density functional theory (DFT) calculations. We address coherent interfaces between a fcc iron or nickel matrix and a frequently observed carbide, the ${M}_{23}{\mathrm{C}}_{6}$, for which a simplified chemical composition ${\mathrm{Cr}}_{23}{\mathrm{C}}_{6}$ is assumed. The interfacial properties such as the formation and Griffith energies, and the effective Young's modulus are analyzed as functions of the magnetic state of the metal lattice, including the paramagnetic phase of iron. Interestingly, a simpler antiferromagnetic phase is found to exhibit similar interfacial mechanical behavior to the paramagnetic phase. A linear dependence is determined between the surface (and interface) energy and the variation of the number of chemical bonds weighted by the respective bond strength, which can be used to predict the relative formation energy for the surface and interface with various chemical terminations. Finally, the critical stresses of both intraprecipitate and interfacial fractures due to a tensile loading are estimated via the universal binding energy relation (UBER) model, parametrized on the DFT data. The validity of this model is verified in the case of intraprecipitate fracture, against results from DFT tensile test simulations. In agreement with experimental evidences, we predict a much stronger tendency for an interfacial fracture for this carbide. In addition, the calculated interfacial critical stresses are fully compatible with available experimental data in steels, where the interfacial carbide-matrix fracture is only observed at incoherent interfaces.

A theoretical approach to quantify the effect of random cracks on rock deformation in uniaxial compression

Cracks have a significant effect on the uniaxial compression of rocks. Thus, a theoretically analytical approach was proposed to assess the effects of randomly distributed cracks on the effective Young's modulus during the uniaxial compression of rocks. Each stage of the rock failure during uniaxial compression was analyzed and classified. The analytical approach for the effective Young's modulus of a rock with only a single crack was derived while considering the three crack states under stress, namely, opening, closure-sliding, and closure-nonsliding. The rock was then assumed to have many cracks with randomly distributed direction, and the effect of crack shape and number during each stage of the uniaxial compression on the effective Young's modulus was considered. Thus, the approach for the effective Young's modulus was used to obtain the whole stress–strain process of uniaxial compression. Afterward, the proposed approach was employed to analyze the effects of related parameters on the whole stress–stain curve. The proposed approach was eventually compared with some existing rock tests to validate its applicability and feasibility. The proposed approach has clear physical meaning and shows favorable agreement with the rock test results.

Effect of crosslink torsional stiffness on elastic behavior of semiflexible polymer networks.

Networks of semiflexible filaments are building blocks of different biological and structural materials such as cytoskeleton and extracellular matrix. The mechanical response of these systems when subjected to an applied strain at zero temperature is often investigated numerically using networks composed of filaments, which are either rigidly welded or pinned together at their crosslinks. In the latter, filaments during deformation are free to rotate about their crosslinks while the relative angles between filaments remain constant in the former. The behavior of crosslinks in actual semiflexible networks is different than these idealized models and there exists only partial constraint on torques at crosslinks. The present work develops a numerical model in which two intersecting filaments are connected to each other by torsional springs with arbitrary stiffness. We show that fiber networks composed of rigid and freely rotating crosslinks are the limiting case of the present model. Furthermore, we characterize the effects of stiffness of crosslinks on effective Young's modulus of semiflexible networks as a function of filament flexibility and crosslink density. The effective Young's modulus is determined as a function of the mechanical properties of crosslinks and is found to vanish for networks composed of very weak torsional springs. Independent of the stiffness of crosslinks, it is found that the effective Young's modulus is a function of fiber flexibility and crosslink density. In low density networks, filaments primarily bend and the effective Young's modulus is much lower than the affine estimate. With increasing filament bending stiffness and/or crosslink density, the mechanical behavior of the networks becomes more affine and the stretching of filaments depicts itself as the dominant mode of deformation. The torsional stiffness of the crosslinks significantly affects the effective Young's modulus of the semiflexible random fiber networks.

Effect of interfacial transition zone on the Young's modulus of carbon nanofiber reinforced cement concrete

Identifying the properties of the region where the cement paste meets the aggregate surface (interfacial transition zone, ITZ) is critical to understanding the strength and fracture behavior of carbon nanofiber (CNF) reinforced cement concrete. In this study, the finite element method is employed to investigate the effect of the ITZ on the Young's modulus of cement concrete made with CNF. The numerical models for cement concrete with and without CNF are constructed based on the digital image processing technique. To consider the interface effect, the concept of “effective aggregate” is put forward, namely, the Young's modulus and Poisson's ratio for each aggregate particle are replaced by an effective Young's modulus and effective Poisson's ratio, in which the effect of thickness and the Young's modulus of ITZ is taken into account in an averaged manner. Then, the quantitative nanomechanical mapping (based on atomic force microscopy) technique is adopted to measure the Young's modulus and thickness of ITZ with and without CNFs, which are further used as the input parameters in the numerical model. The numerical simulation results are verified by experimental testing, which indicates that the ITZ effect should be considered when implementing the numerical simulation. In addition, this analysis shows that compared with the plain cement concrete, CNFs can greatly enhance the mechanical properties of ITZ, which will in turn improve the Young's modulus of cement concrete significantly. Finally, the effect of thickness and Young's modulus of ITZ on the Young's modulus of CNF reinforced cement concrete is also discussed.

Non-enzymatic cross-linking of collagen type II fibrils is tuned via osmolality switch.

ABSTRACTAn important aspect in cartilage ageing is accumulation of advanced glycation end products (AGEs) after exposure to sugars. Advanced glycation results in cross‐links formation between the collagen fibrils in articular cartilage, hampering their flexibility and making cartilage more brittle. In the current study, we investigate whether collagen cross‐linking after exposure to sugars depends on the stretching condition of the collagen fibrils. Healthy equine cartilage specimens were exposed to l‐threose sugar and placed in hypo‐, iso‐, or hyper‐osmolal conditions that expanded or shrank the tissue and changed the 3D conformation of collagen fibrils. We applied micro‐indentation tests, contrast enhanced micro‐computed tomography, biochemical measurement of pentosidine cross‐links, and cartilage surface color analysis to assess the effects of advanced glycation cross‐linking under these different conditions. Swelling of extracellular matrix due to hypo‐osmolality made cartilage less susceptible to advanced glycation, namely, the increase in effective Young's modulus was approximately 80% lower in hypo‐osmolality compared to hyper‐osmolality and pentosidine content per collagen was 47% lower. These results indicate that healthy levels of glycosaminoglycans not only keep cartilage stiffness at appropriate levels by swelling and pre‐stressed collagen fibrils, but also protect collagen fibrils from adverse effects of advanced glycation. These findings highlight the fact that collagen fibrils and therefore cartilage can be protected from further advanced glycation (“ageing”) by maintaining the joint environment at sufficiently low osmolality. Understanding of mechanochemistry of collagen fibrils provided here might evoke potential ageing prohibiting strategies against cartilage deterioration. © 2018 The Authors. Journal of Orthopaedic Research Published by Wiley Periodicals, Inc. on behalf of Orthopaedic Research Society. J Orthop Res 36:1929–1936, 2018.

Analysis of Dynamic Behavior of the Finite Elastic Metamaterial-Based Structure With Frequency-Dependent Properties

For practical applications of the elastic metamaterials, dynamic behavior of finite structures made of elastic metamaterials with frequency dependent properties are analyzed theoretically and numerically. First, based on a frequency-dependent mass density and Young's modulus of the effective continuum, the global dynamic response of a finite rod made of elastic metamaterials is studied. It is found that due to the variation of the effective density and Young's modulus, the natural frequency distribution of the finite structure is altered. Furthermore, based on the spectral approach, the general wave amplitude transfer function is derived before the final transmitted wave amplitude for the finite-layered metamaterial structure with decreasing density is obtained using the mathematical induction method. The analytical analysis and finite element solutions indicate that the increased transmission wave displacement amplitude and reduced stress amplitude can be controlled by the impedance mismatch of the adjacent layers of the layered structure.

Biocompatible porous titanium scaffolds produced using a novel space holder technique.

We describe a new fabrication strategy for production of porous titanium scaffolds for skeletal implants which provides a promising new approach to repair and remodel damaged bone tissue. The new strategy involves powder sintering of titanium powder, employing pharmaceutical sugar pellets as temporary space holders, to facilitate production of porous scaffolds with structures optimized for mechanical performance and osseointegration of implants. The spherical sugar pellets, with controlled size fractions and excellent biocompatibility, are easily removed by dissolution prior to sintering providing an ideal space holder material for controlled synthesis of titanium scaffolds with desired porosities and pore sizes. The scaffolds contain pores with high degrees of sphericity and interconnectivity which impart excellent mechanical properties and superior biocompatibility to the structures. Scaffolds with 40% porosity and a pore size range of 300-425 µm exhibited an effective Young's modulus of 16.4 ± 3.5 GPa and strength of 176 ± 6 MPa, which closely mimics the properties of human bone, and were also able to support cell adhesion, viability and spreading in cell culture tests. Porous titanium scaffolds manufactured by this approach have excellent potential for hard tissue engineering applications. © 2018 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 2796-2806, 2018.

Study on the size dependent effective Young modulus by EPI method based on modified couple stress theory

Various experimental and theoretical researches have been shown the size-dependence behavior of the effective Young modulus (EYM) in the micron and sub-micron scales. One of the most accurate methods is the electrostatic pull-in instability (EPI) method that is based on the bending of the classical beam under the electrostatic force. In this paper, the modified couple stress theory (MCST) is employed to calculate the EYM of silicon nanocantilevers. The MCST compensates the inability of the classical continuum mechanic to predicting the size-dependent behavior of the nano-scale structures. Next, as a case study the EYM of silicon nanocantilevers have been calculated and results compared with classical EPI. The governing equation is solved by the Galerkin method and obtained results show significant size-dependent behavior in the EYM. From the other hand, a new value for the material length scale parameter is introduced based on the dimension of the crystal or grain size of the material.

Structural and Mechanical Comparison of Human Ear, Alar, and Septal Cartilage.

In the human ear and nose, cartilage plays a key role in establishing its form and function. Interestingly, there is a noticeable paucity on biochemical, structural, and mechanical studies focused on facial cartilage. Such studies are needed to provide elementary knowledge that is fundamental to tissue engineering of cartilage. Therefore, in this study, a comparison is made of the biochemical, structural, and mechanical differences between ear, ala nasi, and septum on the extracellular matrix (ECM) level. Cartilage samples were harvested from 10 cadaveric donors. Each sample was indented 10 times with a nanoindenter to determine the effective Young's modulus. Structural information of the cartilage was obtained by multiple-photon laser scanning microscopy capable of revealing matrix components at subcellular resolution. Biochemistry was performed to measure glycosaminoglycan (GAG), DNA, elastin, and collagen content. Significant differences were seen in stiffness between ear and septal cartilage (P = 0.011) and between ala nasi and septal cartilage (P = 0.005). Elastin content was significantly higher in ear cartilage. Per cartilage subtype, effective Young's modulus was not significantly correlated with cell density, GAG, or collagen content. However, in septal cartilage, low elastin content was associated with higher stiffness. Laser microscopy showed a distinct difference between ear cartilage and cartilage of nasal origin. Proposed methods to investigate cartilage on the ECM level provided good results. Significant differences were seen not only between ear and nasal cartilage but also between the ala nasi and septal cartilage. Albeit its structural similarity to septal cartilage, the ala nasi has a matrix stiffness comparable to ear cartilage.

Tuning properties and behavior of magnetron sputtered Zr-Hf-Cu metallic glasses

Amorphous ternary Zr-Hf-Cu thin-film alloys with glass-like behavior were deposited by non-reactive conventional dc and high-power impulse magnetron co-sputtering using three unbalanced magnetrons equipped with Zr, Hf and Cu targets. The Zr and Hf targets were operated in a dc regime while the Cu target in a high power impulse regime. Two series of films with a gradually increasing Hf/(Hf+Zr) ratio at 46 at.% Cu and 59 at.% Cu were deposited. The effect of the elemental composition on the structure, thermal behavior, mechanical and surface properties, electrical resistivity and oxidation resistance was systematically investigated. We found a clear correlation among the evolution of the glass transition temperature, crystallization temperature, hardness and effective Young's modulus with increasing Hf/(Hf+Zr) ratio. A linear increase of these quantities is attributed to an increase of the average bond energy in the films as Hf gradually substitutes Zr. The Zr-Hf-Cu thin-film metallic glasses exhibit enhanced hardness (up to 7.8 GPa), enhanced thermal stability and oxidation resistance, very smooth (surface roughness down to 0.2 nm) and hydrophobic surface (water contact angle up to 109°), and very low electrical resistivity (lower than 1.9 × 10−6 Ωm).

Micromechanical modeling of 3D printable interpenetrating phase composites with tailorable effective elastic properties including negative Poisson's ratio

3D printable two-phase interpenetrating phase composites (IPCs) are designed by embedding a 3D periodic re-entrant lattice structure (as the reinforcing phase) in a matrix phase. These IPCs display the cubic or tetragonal symmetry. A micromechanical model is developed to evaluate effective elastic properties of the IPCs. Effective Young's moduli, shear moduli and Poisson's ratios (PRs) of each IPC are determined from the effective stiffness and compliance matrices of the composite, which are obtained through a homogenization analysis using a unit cell-based finite element (FE) model incorporating periodic boundary conditions. The FE simulation results are also compared with those based on various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. The effective properties of the IPC can be tailored by adjusting five geometrical parameters, including two strut lengths, two re-entrant angles and one strut diameter, and elastic properties of the two constituent materials. The numerical results reveal that IPCs with a negative PR can be generated by using a compliant matrix material and large re-entrant angles. In addition, it is found that the two re-entrant angles can greatly affect other effective elastic properties of the IPC: the effective shear modulus can be enhanced, while the effective Young's modulus can be enhanced or compromised with the increase of the re-entrant angles. Furthermore, it is seen that by adjusting one of the two re-entrant angles or one of the two strut lengths, the material symmetry exhibited by the IPC can be changed from cubic to tetragonal.

Two‐Layered Tubes from Cubic Crystals: Auxetic Tubes

Effective Young's modulus and Poisson's ratios of two‐layered cylindrical hollow tubes made of cubic crystals (auxetics and nonauxetics) are considered. An analysis of longitudinal tension of stretching tubes is performed within the framework of curvilinear‐anisotropic elasticity and Saint‐Venant's approximation. Analytical dependences of effective Young's modulus on the compliance coefficients of the initial crystals and layer thickness as ratio of composites auxetics–nonauxetics are obtained. Deviations from the “rule of mixtures” predictions which increase with increasing Young's modulus of initial nonauxetics are demonstrated. It is found that effective Poisson's ratios of two‐layered tubes depend on the ratio of their thicknesses, the dimensionless combinations of compliance coefficients and a dimensionless radial distance. An effect of tube components on negativeness of effective Poisson's ratio of the composite auxetics–nonauxetics proved to be strongly dependent on the value of Young's modulus for nonauxetic component. It is shown that effective Poisson's ratios for some characteristics of the initial crystals and ratios of layer thicknesses may fall outside the limits on Poisson's ratios of isotropic materials. It is shown that many two‐layered tubes composed of pairs of nonauxetics can have large negative effective Poisson's ratios.

Nanoporous Au foams: Variation of effective Young's modulus with ligament size

This work focuses on the effects of ligament size on the mechanical behavior of NP Au foams. NP Au structures with ligament diameter between 5 and 200nm have been fabricated by selective Ag dissolution from Ag70Au30 alloys prepared by mechanical alloying and subsequent annealing. Nanoindentation experiments indicate that the effective Young's modulus increases as the ligament thickness decreases. The stiffening of NP Au foams with fine ligaments is ascribed to size effects connected with surface stress states. It is shown that a phenomenological model accounting for disorder and surface contributions to Young's modulus correctly predicts the observed behavior.

Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets

Abstract This paper presents static bending and compressive buckling analyses of functionally graded multilayer graphene nanoplatelet (GPL)/polymer composite plates within the framework of the first-order shear deformation theory. The GPL weight fraction shows a layer-wise change along the thickness direction with GPLs uniformly dispersed in the polymer matrix in each individual layer. The effective Young's modulus of the nanocomposites is estimated through the Halpin-Tsai micromechanics model while the effective Poisson's ratio is determined by the rule of mixture. Analytical solutions are obtained for the static deflection and critical buckling load of the simply supported functionally graded GPL/polymer plates by using the Navier solution technique. Numerical results show that GPL distribution pattern, weight fraction, and geometry and size have significant influences on the bending and buckling behaviors of the functionally graded GPL reinforced nanocomposite plate.

21.02: Strengthening of orthotropic steel decks using UHPC: UHPC‐concrete instead of asphalt layer for additional at least 50 years in service

ABSTRACTOrthotropic steel bridge decks for slender and long spanned girder bridges were frequently built in the 60ties and 70ties of the last century in Europe. In the design of such bridge decks only the ultimate load carrying capacity was considered, without fatigue aspects. Due to the dramatic increase of heavy traffic in the European road network, sometimes the calculated remaining fatigue life is exhausted, after only 50 years of service life.In the paper the relevant results of a research project are presented, with the challenging aim to increase the service life of such orthotropic bridge decks to at least 50 years after strengthening. The research activities were based on a very slender orthotropic deck, with a slenderness of elr/tdp = 36 for the deck plate. Two significant details for fatigue of such a representative bridge deck have been analysed. Detail D1 represents the welded connection of the longitudinal rib to the deck plate and Detail D2 is the welded connection of the longitudinal rib to the cross girder. Extensive numerical studies were done for the strengthening solution with an UHPC‐concrete layer. First the present remaining service life was calculated using a finite element model of the steel deck. The beneficial effect of the asphalt layer is considered by an increased wheel contact area. The current fatigue load model FLM‐4 from the Eurocode with 5 lorry types and 3 different axle types was executed and the gross weight of each lorry type was adapted to weigh in motion measurements at an Austrian highway bridge. For determining the stress reduction factors in the details D1 and D2 after strengthening the finite element model had to be extended with the UHPC‐concrete layer. The concrete cracking was conservatively considered with an effective Young modulus Ec,eff = Ec/4. For both details at least 50 years in service can be guaranteed with an UHPC‐pavement that has a thickness of 80mm. Based on these studies full scale tests on an orthotropic deck specimen were done, including overload effects (increased axle loads) and severe temperature effects (simulation of a cold rain event on a very hot summer day) to stimulate concrete cracking. The full scale tests together with the numerical studies showed very good results with regard to the remaining fatigue life. Therefore in the near future a prototype application on an Austrian highway bridge is intended.