Elastic Moduli E1 Research Articles

On the Use of Foam Rubber for Sealing Applications

O-rings made from foam rubber are often used in sealing applications. Foam rubber have low (macroscopic) elastic modulus E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_0$$\\end{document} resulting in a low nominal contact pressure when squeezed against a countersurface. In most cases the foam rubber is covered by a thin surface film with the effective elastic modulus E1>E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_1 > E_0$$\\end{document}. We show that the nominal contact pressure may not be high enough for the contact area to percolate and the O-ring seal will leak. For the leakage calculations we use the Persson multiscale contact mechanics theory, and the (modified) Bruggeman effective medium theory for the fluid flow conductivity. The experimental input for the theory are surface roughness power spectrum, which was obtained from stylus topography measurements, and the elastic properties (E0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_0$$\\end{document} and E1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_1$$\\end{document}) of the rubber O-ring. As an application of this calculation method, we have used the preliminary as well as the final results of the laboratory gas tightness tests of the 136 New Small Wheel Micromegas Quadruplets performed at CERN, from February 2019 to May 2021, in the framework of the ATLAS Experiment upgrade. In the integration quality control, a novel method for gas tightness measurement, that we have called “Flow Rate Loss”, has been used as a baseline method.Graphical

Discrete Element Modeling of Thermally Damaged Sandstone Containing Two Pre-Existing Flaws at High Confining Pressure

An underground coal gasification (UCG) process is strongly exothermic, which will cause thermal damage on rock cap. We proposed a new thermal damage numerical model based on a two dimension particle flow code (PFC2D) to analyze the inception and extension of cracks on pre-cracked red sandstone, which were thermally treated at a temperature of 25~1000 °C. The results indicated that: (1) a thermal damage value DT obtained by extracting the thermal crack area of scanning electron microscope (SEM), which can be used as an indicator of the degree of thermal damage of the sandstone; (2) a thermal damage numerical model established by replacing the flat-joint model with the smooth-joint model based on the thermal damage value DT, this approach can properly simulate the mechanical behavior and failure patterns of sandstone; (3) the critical temperature for strength reduction was 750 °C. The peak strength increased as pre-treatment temperature increased from 25 to 750 °C and then decreased. The elastic modulus E1 decreased with the increasing thermal treatment temperature; (4) micro-scale cracks initiate from the tip of the prefabricated fissure, and expand along the direction of prefabricated fissure, finally developing into macroscopic fracture. This approach has the potential to enhance the predictive capability of modeling and presents a reliable model to simulate the mechanical behavior of thermally damaged sandstones, thereby offering a sound scientific basis for the utilization of space after UCG.

Anisotropic mechanical characterization of human skin by in vivo multi-axial ring suction test

Human skin is a soft tissue behaving as an anisotropic material. The anisotropy emerges from the alignment of collagen fibers in the dermis, which causes the skin to exhibit greater stiffness in a certain direction, known as Langer’s line. The importance of determining this anisotropy axis lies in assisting surgeons in making incisions that do not produce undesirable scars. In this paper, we introduce an open-source numerical framework, MARSAC (Multi-Axial Ring Suction for Anisotropy Characterization: https://github.com/aflahelouneg/MARSAC), adapted to a commercial device CutiScan CS 100® that applies a suction load on an annular section, causing a multi-axial stretch in the central zone, where in-plane displacements are captured by a camera. The presented framework receives inputs from a video file and converts them into displacement fields through Digital Image Correlation (DIC) technique. From the latter and based on an analytical model, the method assesses the anisotropic material parameters of human skin: Langer’s line ϕ, and the elastic moduli E1 and E2 along the principal axes, providing that the Poisson’s ratio is fixed. The pipeline was applied to a public data repository, https://search-data.ubfc.fr/femto/FR-18008901306731-2021-08-25_In-vivo-skin-anisotropy-dataset-for-a-young-man.html, containing 30 test series performed on a forearm of a Caucasian subject. As a result, the identified parameter averages, ϕˆ=40.9±8.2∘ and the anisotropy ratio E1ˆ/E2ˆ=3.14±1.60, were in accordance with the literature. The intra-subject analysis showed a reliable assessment of ϕ and E2. As skin anisotropy varies from site to site and from subject to subject, the novelty of the method consists in (i) an optimal utilization of CutiScan CS 100® probe to measure the Langer’s line accurately and rapidly on small areas with a minimum diameter of 14mm, (ii) validation of an analytical model based on deformation ellipticity.

Identification of Primary Failure Modes of Tunnel System and Influence of Supporting Structures on Tunnel System Reliability using Multiple Response Surfaces

A method of calculating the failure probability of the tunnel system combining finite element numerical simulation with multiple response surface method (MRSM) and Monte-Carlo simulation (MCS) is presented. The applicability of the proposed methodology is verified through a subway interval soft rock tunnel in Qingdao, China. The sensitivity of Monte-Carlo sampling number and coefficients of variation for rock masses on the failure probability of tunnel system is conducted. The primary failure modes in tunnel system are identified by reanalyzing the failure samples. The simulation results demonstrate that the failure probability of a tunnel system within soft upper and hard lower surrounding rock mass is mainly attributed to the soft upper part of the surrounding rock. The coefficients of variation of the elastic modulus E1 and the internal friction angle ϕ1 of the pebble layer (soft upper part) have significant effect on the failure probability. The failure probability of tunnel system increases as the coefficients of variation of E1 and ϕ1; increase. Two primary failure modes are found to contribute to the tunnel system reliability. The effect of rock bolt length L and pipe-roof thickness H on tunnel system reliability and two primary failure modes as well are investigated. The simulation results indicate that both the enhancements in L and H tend to be more effective than the enhancement in either L or H if a small target failure probability of tunnel system is expected. The supporting structures design can be performed based on the potential sets of (L, H) satisfying target failure probability.

Influence of material properties and geometric parameters of an impact pair on contact acceleration during a low-velocity impact

Experimental equipment that can provide suitable acceleration peaks (APs) and acceleration pulse widths (AWs) is required for impact studies. It is necessary to design suitable structures and select appropriate materials of the impact pair for experimental equipment. To propose the control strategies of the AP and AW, the effects of the material properties and geometric parameters of the impact pair on the contact acceleration during low-velocity impacts were investigated. The density ρ1 and velocity v of the projectile, and the elastic modulus E2 and yield strength A2 of the target were the dominant factors affecting the AP. The ρ1, A2, and E2 were the primary factors influencing the AW. The AP increased with a decrease in the ρ1 and increases in the v and elastic modulus E1 of the projectile and the thickness H, E2, A2, strain-hardening constant B2, and strain-hardening index n2 of the target. The AW increased with the ρ1 and decreased with the H, E2, and A2. Based on the elastic stress wave and contact mechanics, the influences of the primary factors on the AP and AW were explained. The strategies proposed in this work agreed with the simulation results and the literature.

Quality of wheat breads enriched with flour from germinated amaranth seeds.

Amaranth flour from germinated (GA) and non-germinated (A) seeds (0%-C, 5%, 15%, 25%) were mixed with wheat flour for breadmaking. Fermentation parameters of dough (time-tf, maximum volume-Vmax) were obtained. Specific volume (Vsp) of breads, crust color, texture and relaxation of crumb were analyzed. A high amount of germinated amaranth flour decreased Vmax and increased tf, obtaining breads with low Vsp and darkness crust. A firmed and chewy crumb, although with a more aerated structure (high area occupied by alveoli) was obtained. The GA25 bread presented the softer crumb. The elastic modulus-E1 of crumb increased and the relaxation time-T1 decreased with higher amounts of amaranth flour, suggesting the formation of a more structured crumb; mainly in the case of non-germinated amaranth flour. Wheat flour resisted the inclusion of 25% of germinated amaranth seeds (GA25) without substantial changes in bread quality.

Experimental Study on Influence of Unloading Rate on Creep Characteristics of Marble under High Stress

In the engineering of high stress area, the measures to control the stability of surrounding rock by reducing excavation footage and excavation speed are to adjust the unloading rate of surrounding rock caused by excavation. In this study, unloading creep tests of marble under high stress conditions were carried out to study the effect of unloading rate. Research results showed that the axial and lateral instantaneous strain and creep strain of the sample increased with the increase of unloading rate; the lateral creep characteristic of marble under unloading condition was stronger than that of axial creep characteristic, and it was more obvious with the increase of unloading rate; the failure of specimens under unloading creep condition was mainly caused by the rapid increase of lateral strain, and the brittleness of rock was increasing with the increase of unloading rate. The Burgers model was used to describe the creep curves of specimens, and the variation of the parameters with the unloading rate was analyzed. The fitting results showed that the instantaneous elastic modulus E1, E'1 and the viscosity coefficients η1, η'1 all decreased with the increase of the unloading rate, which can be described by linear relationship within the unloading rate range of this experiment. Compared with the time of whole creep tests, the time for each specimen to enter the steady-state creep was similar, it was considered that the effect of unloading rate on η2/E2 and η'2/E'2 can be ignored.

Composite Piezoelectric Energy Harvesters with Symmetric Angle‐Ply Stacking Sequences and Variable Through‐the‐Thickness Poisson's Ratios

Herein, the effect of symmetric carbon fiber composites laminates with angle‐ply stacking sequences ([±β/±θ]S) in the design of composite piezoelectric energy harvesters (PEHs) is evaluated. Some of those specific stacking sequences also feature negative Poisson's ratio (NPR) or near zero Poisson's ratio (NZPR) through the thickness for ply angles θ < 45°. Six different architectures with similar in‐plane elastic modulus E1 and different positive Poisson's ratio and NPR v13 values are considered here. Finite element models are developed to understand the distribution of the voltage density of the laminates with the different stacking sequences and their bending properties. Experimental tests (three‐point bending and vibration) are also performed. Both the simulations and the experimental results show that the PEH with the stacking sequences of near zero v13 generate the highest power compared with the other composite energy harvesters. The maximum voltage frequency response function (FRF) happens at the fundamental resonance, and the PEH with near zero v13 has also the lowest resonance frequency compared with the other stacking sequences.

Vertical Fibrous Morphology and Structure-Function Relationship in Natural and Biomimetic Suction-Based Adhesion Discs

Summary Recent years have seen rapid development in bio-inspired materials for adhesion. However, it remains challenging to realize robust adhesion on rough aquatic surfaces. An inspiring natural model is the remora fish, which has evolved to retain powerful adhesion to hosts using a dorsal suction disc. We find that the remora suction disc has a unique fibrous architecture of vertically oriented collagen fibers that enable anisotropic mechanical properties and enhanced adhesion performance. In the engineered prototype, vertically oriented nylon fibers are embedded into the soft silicone matrix using electrostatic flocking. The anisotropic mechanical properties are validated in both natural and biomimetic suction discs. Furthermore, the biomimetic suction disc demonstrates an enhanced adhesion function with a maximum 62.5% increase in pull-off force and a 340% increase in attachment time compared with the silicone control. This work can shed light on natural adhesion mechanisms and inspire novel designs for aquatic soft adhesives and actuators.

Viscoelastic Properties of Asphalt Mixtures with Different Modifiers at Different Temperatures Based on Static Creep Tests

To obtain the viscoelastic parameters of asphalt mixtures and analyze the effect of temperatures and modifiers on viscoelastic properties of asphalt mixtures, the creep compliances of the neat asphalt mixture (AM), compound diatomite and basalt fibers reinforced asphalt mixture (DBFAM), and styrene-butadiene-styrene modified asphalt mixture (SBSAM) were tested and calculated by the static creep tests. And the creep compliances of the three asphalt mixtures at −20 °C, −10 °C, and 0 °C are deducted by the time–temperature equivalence principle (TTEP) and Arrhenius equation. Further, the relaxation modulus of the three asphalt mixtures from −20 °C to 50 °C at 10 °C increments are calculated by the convolution integral and Simpson method. Subsequently, the Burgers model, the generalized Kelvin model, and the generalized Maxwell model are applied to analyze the viscoelastic properties of the three asphalt mixtures at different temperatures. The results show that the generalized Kelvin model and the generalized Maxwell model are superior to the Burgers model in describing the variation of viscoelastic properties of asphalt mixtures with loading time. At low temperatures, asphalt mixtures have excellent properties in resisting permanent deformation and releasing internal stress. Besides, the addition of SBS modifier and compound diatomite and basalt fibers modifier can significantly raise the viscosity η1 and the elastic modulus E1 of the asphalt mixture, respectively.

CONCENTRATION OF STRESSES NEAR V-SHAPED ELEMENTS

The study of stress concentrators, especially those that cause the formation of singularities of σ→∞ form, is of great scientific and applied importance. The most famous representative of such stress concentrators is the crack, which is the subject of study of fracture mechanics. Cracks can be normal, located in a homogeneous material, interfacial, intersecting the phase plane between two different materials. Depending on this, stress fields are formed with different features. Another class of similar stress concentrators is V-shaped elements that form a dihedral angle with a disclosure angle greater than zero. V-shaped elements can be formed in both homogeneous and dissimilar materials. The singularity features depend on the mechanical properties of the materials and the angles occupied by these materials. If the opening angle is zero, then the corresponding formulas are transferred to the well-known formulas for cracks. The next class of stress concentrators forming the singularity is the internal elements with V-shaped material boundaries. Such elements are formed around non-metallic inclusions with sharp corners, in fibrous composite materials at the ends of the fibers. Unlike the previous class, in this case there are no empty sectors. However, the resulting formulas transfer into the well-known expressions, if the mechanical properties of one of the materials tend to zero. Thus, all classes of tasks related to the formation of a singularity of a σ→∞ form can be considered as one common task with an increased number of parameters. Such work is done in this article. This made it possible to obtain new patterns of stress state and to determine the directions for the further development of mechanics destruction. As an example, using the complex potentials method with the application of the Kolosov-Muskhelishvili equations, a theoretical analysis of the stress state at the top of the V-shaped boundary separating two homogeneous materials with different normal elastic moduli E1 and E2 was carried out. The calculation showed that in the local zone near the top of the angle, the straightened state acquires a singular character, the stress distribution is described by terms of the form σ ≈ К/rλ, and the parameters of the singularity λ1, λ2, λ3 depend on the ratio of the elastic characteristics of the materials. Relevant patterns are studied.

Dynamic analysis of indentation rolling resistance of steel cord rubber conveyor belt

To study the variation trend of the indentation rolling resistance of a rubber conveyor belt under different environmental temperatures, the sinusoidal compression displacement test was first carried out on the rubber matrix at six temperatures between -20 °C and 40 °C by a high and low temperature universal testing machine. Elastic modulus E1, E2 and loss factor tan θ of the rubber matrix were identified using the Fourier series. Then, the dynamic contact characteristics between the idling roller and conveyor belt were analyzed by the viscoelastic mechanics theory. Hence, the calculation equation of the indentation rolling resistance in the full thickness direction of the conveyor belt was deduced. Finally, a practical calculation and experimental verification of the indentation rolling resistance of the steel cord rubber conveyor belt at different temperatures were conducted. The results showed that the drop of the indentation rolling resistance of the conveyor belt was significant when the temperature was increased in the range of -20–10 °C. In the range of 10–40 °C, the influence of the increase of the ambient temperature on the indentation rolling resistance was relatively weak. Additionally, it is found that the contact force in the vertical direction and the idling roller diameter are important factors that affect the indentation rolling resistance of the conveyor belt. The influence of belt speed on the indentation rolling resistance is weak.

A dimensionless analysis of shear modulus and stress distribution for anisotropic materials

ABSTRACTThe effect of various off­axis angles and lamina material properties on the shear modulus and the stress distribution of a circular cut-out in an orthotropic composite plate under shear loadings are presented. Based on the generalized Hooke's law, the generalized plane stress condition and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the laminate shear modulus and the stress distribution along the boundary of the circular cut-out within the laminate under shear loading. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high-precision requirements in engineering applications.

A dimensionless analysis of stress distribution for constrained pressure in an orthotropic plate

The effect of the properties of lamina material on the stress distribution of the orthotropic composite plate containing a circular cut-out under constrained pressure is investigated. Based on the generalised Hooke's law, the generalised plane stress condition and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the stress distribution along the boundary of the cut-out in the composite plate under constrained pressure. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

A dimensionless analysis of Poisson’s ratio and stress distribution for anisotropic materials

The effect of various offaxis angles and lamina material properties on the Poisson’s ratio and the stress distribution of a circular cutout in an orthotropic composite plate under off-axis loading are presented. Based on the generalized Hook’s law, the generalized plane stress condition and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12, and ν12on the Poisson’s ratio and the stress distribution along the boundary of the circular cutout under various off-axis loadings. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

A Dimensionless Analysis of Young's Modulus and Stress Distribution for Orthotropic Materials

The effect of various offaxis angles and lamina material properties on the axial and transverse modulus of the orthotropic lamina under off-axis loading is studied. Also, the stress distribution of the orthotropic composite plate containing a circular cutout with normal pressure distributed uniformly along the opening edge is investigated. Through the generalized Hooke’s law and plane stress condition, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the axial and transverse modulus of the orthotropic lamina under various off-axis loadings. Moreover, based on the generalized Hooke’s law, the generalized plane stress and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the stress distribution along the boundary of the circular cutout of the orthotropic plate with normal pressure distributed uniformly along the opening edge. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

A Dimensionless Analysis of Stress Distribution for Hydrostatic Tension in an Orthotropic Plate

The effect of lamina material properties on the stress distribution of the orthotropic composite plate containing a circular cutout under hydrostatic tension is investigated. Based on the generalized Hooke’s law, the generalized plane stress condition and the complex variable method, a dimensionless analysis is used to evaluate the influence of various elastic moduli E1, E2, G12 and ν12 on the stress distribution along the boundary of the cutout in the composite plate under hydrostatic tension. The results obtained from this dimensionless analysis provide a set of general design guidelines for structural laminates with high precision requirements in the engineering applications.

Analysis of In-plane Elastic Modulus for a Hexagonal Honeycomb Core (2nd Report, Analysis of Young's Modulus and Shear Modulus)

For honeycomb subjected to in-plane loading, there exist deformations in the height direction for cell walls due to effect of Poisson's ratio. Because these deformations are different for adjacent walls, the elastic modulus of honeycomb should be analyzed as a 3-dimensional problem. In this paper, the method of analysis for the equivalent elastic modulus E1 proposed by authors in the 1st report, in which the effect of height h of the honeycomb core on the elastic modulus is taken into account, is applied to theoretical formula for calculating Young's modulus E1 and shear modulus G12. Then, the validity of the proposed theoretical formula for elastic moduli E1 and G12 is verified comparing with the numerical results by FEM.

Viscoelastic Behavior of Fibers During Woven Fabric Bagging

The aim of this paper is to study the viscoelastic behavior of fibers during the woven fabric bagging process through a series of experiments and a mathematical model to simulate bagging under the testing conditions. Through a large number of computational experiments, the elastic modulus E1 , viscoelastic modulus E2, fiber relaxation time T, and three weighting coefficients ( k3, k4, k5) are determined for six woven fabrics made from different fibers. A comparison of the experimental measurements with the predicted bagging behavior of the fabrics reveals that the mathematical model is able to predict bagging behavior with reasonable accuracy. The results show that the viscoelastic behav ior of fibers in the six fabrics is significantly different during bagging. Nylon and polyester have a high elasticity ratio ( E, ), a low viscoelasticity ratio ( E2), and a large relaxation time T. Silk, viscose, and cotton fibers have a low elasticity ratio ( E, ), a high viscoelas ticity ratio ( E2), and a small relaxation time T. For cotton and wool, with the same level of viscoelasticity ( E2), the stress relaxation process is determined by relaxation time T. These results suggest that fiber viscoelastic behavior plays a key role in determining fabric rheological behavior during bagging.

Intervertebral disc response to cyclic loading--an animal model.

The viscoelastic response of a lumbar motion segment loaded in cyclic compression was studied in an in vivo porcine model (N = 7). Using surgical techniques, a miniaturized servohydraulic exciter was attached to the L2-L3 motion segment via pedicle fixation. A dynamic loading scheme was implemented, which consisted of one hour of sinusoidal vibration at 5 Hz, 50 N peak load, followed by one hour of restitution at zero load and one hour of sinusoidal vibration at 5 Hz, 100 N peak load. The force and displacement responses of the motion segment were sampled at 25 Hz. The experimental data were used for evaluating the parameters of two viscoelastic models: a standard linear solid model (three-parameter) and a linear Burger's fluid model (four-parameter). In this study, the creep behaviour under sinusoidal vibration at 5 Hz closely resembled the creep behaviour under static loading observed in previous studies. Expanding the three-parameter solid model into a four-parameter fluid model made it possible to separate out a progressive linear displacement term. This deformation was not fully recovered during restitution and is therefore an indication of a specific effect caused by the cyclic loading. High variability was observed in the parameters determined from the 50 N experimental data, particularly for the elastic modulus E1. However, at the 100 N load level, significant differences between the models were found. Both models accurately predicted the creep response under the first 800 s of 100 N loading, as displayed by mean absolute errors for the calculated deformation data from the experimental data of 1.26 and 0.97 percent for the solid and fluid models respectively. The linear Burger's fluid model, however, yielded superior predictions particularly for the initial elastic response.