Small Deformation Range Research Articles

Shear and shear-induced normal responses of origami cylinders relate to their structural asymmetries

Origami cylinders have been studied extensively under compression, however, their normal force response under shear deformation is still ill-understood. We experimentally studied the shear-induced normal force of these systems and provided a simple model to predict this response in Yoshimura and Kresling origami cylinders in the range of small deformations. Besides that, the effect of disorder is little understood in those origami patterns. Therefore, we investigate the disorder effect and show it can lead to diverse normal responses perpendicular to shear deformation in crumpled Yoshimura, with slopes of the force perpendicular to torsion that can be positive, zero, or negative depending on the disordered pattern of folds. The disorder leads to an asymmetry concerning the shearing direction, which we quantified via an asymmetry index from the 2D Fast Fourier transform spectrum of the crease pattern images. This asymmetry index is found to be linearly related to the slope of the normal force-torsion relationship.

A molecular-dynamics-based model for the rate- and crosslink-density-dependent deformation of silicone rubber

Based on molecular dynamics simulations, a two-parameter hyperelastic constitutive model is proposed for silicone rubber and then extended for the rate- and crosslink-density-dependent uniaxial tensile behaviors. Taking into account the effects of crosslinking and entanglement, the total strain energy is decomposed into bonding and van der Waals terms. The simulation results show that the bonding term works at large deformation and prefers the quadratic term in Yeoh model. In contrast, the van der Waals term is found dominating at small deformation range and modeled through the homogenization of Lennard-Jones potentials. The effects of crosslink density and strain rate on model parameters are described by exponential and hyperbolic sine functions, respectively. Equipping parameters identified from molecular dynamics simulations, the model can efficiently describe the strain–stress relations in whole strain range and for all considered strain rates and crosslink densities. The proposed model and strategy should arise applications in description of complex behaviors of elastomers.

Advection-enhanced heat and mass transport from neutrally suspended droplet in simple shear flow

Advection-enhanced heat and mass transport from a single droplet neutrally suspended in a simple shear flow has been studied using high-fidelity numerical simulation. The capillary number ranges from 0.01 to 0.5, which encompasses the entire range of small deformation, large deformation, and breakup of the droplets. The Reynolds number is from 0.01 to 1, including regions of both weak and strong advection. The temperature and mass concentration are modeled as the concentration of a passive scalar released at the droplet surface. Two Schmidt numbers, 10 and 100, are considered, for which flow advection plays a role in the transport of passive scalar. For unbroken droplets, the interaction between the carrier fluid and the suspended droplet leads to several different flows around the droplet. The fluid motions together with scalar diffusion constitute a coupled transport mechanism for passive scalar. The dependence of scalar release rate on Reynolds and Peclet numbers can be roughly described by the correlation for a rigid sphere. For broken droplets, the basic flow features around the droplet during the process of elongation and breakup are similar to those of an unbroken droplet. The variation of the scalar release rate can be decomposed into several stages, corresponding to the process of droplet elongation and breakup. The variation of the scalar release rate exhibits a high correlation with the capillary, Reynolds, and Peclet numbers. This suggests that it is feasible to develop an empirical model that incorporates the effects of the number and size distributions of child droplets after breakup.

Change in the elastic properties of partially saturated limestone during drying conditions

The article presents the results of an experimental study of the water content effect on the elastic properties of a limestone specimen (Young’s modulus and Poisson’s ratio) during drying after its partial saturation. We first constructed the diagrams of water saturation and water loss, then on their basis we selected the partial saturation mode of the specimen. The specimen was subjected to uniaxial compression in the range of small reversible deformations. We chose the loading range of the specimen to exclude the formation and accumulation of microstructural changes (damages) in the material. The tests were carried out at certain intervals during the natural drying of the specimen. The values of the elastic modulus and the Poisson’s ratio were calculated based on the stress-strain diagrams in accordance with the standard STO 05282612-001-2013 adopted at the Chersky Mining Institute of the North SB RAS. The analysis of the test results revealed the features of the mechanical behavior of the limestone specimen, which indicate a disproportionate and even non-monotonic dependence of the elastic properties on the water content. We propose a hypothesis that allows us to explain the detected effects qualitatively.

Uniaxial tensile strain correction of multi-axial warp-knitted fabric

This paper analyzes the error between the theoretical calculated and actual values of single inserting yarn strain of multi-axial warp-knitted fabric under the uniaxial stretching process, and the “open M-shaped curved surface” of error was obtained theoretically. The analysis results show that the error increases with the increase of fabric elongation. The error is smaller in the small deformation range (fabric maximum elongation is 5%) and larger in the large deformation range. In addition, the error is also related to the angle between the single inserting yarn axis and the uniaxial tensile direction. The error varies periodically with the angle ([Formula: see text]), reaching its maximum when it is close to [Formula: see text]. In order to realize the correction of the existing theoretical calculated formula of single inserting yarn strain, the error formula was fitted by combining the laws of errors. The correction of the single inserting yarn strain was successfully achieved by the fitted error formula. The correction equation can correct the inserting yarn at any angle in the fabric strain range of 0–50%. The correction equation has a larger range of use and more accurate results than the theoretical calculated formula for inserting yarn. Finally, the validation was carried out with bias inserting yarn at [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] angles and the results were very good. Therefore, the corrected equation can replace the actual value of bias inserting yarn strain.

Establishment of constitutive model based on Ogden strain energy storage function and its matching with the mechanical properties of polyurethane dielectrics

In order to find the constitutive relationship of mechanical properties suitable for polyurethane dielectric elastomer, the constitutive model of dielectric elastomer based on Ogden strain energy storage function was established. Then taking polyether MDI polyurethane as the research object, the first-order, second-order and third-order Ogden constitutive models were fitted by the preparation and mechanical properties test of polyurethane dielectric elastomer with different soft and hard segment contents. It is found that the second-order Ogden constitutive model fits the stress-strain curve of polyurethane dielectric elastomer well, and the highest modified fitting coefficient is as high as 0.9996. At the same time, we found that the fitting effect of the third-order Ogden constitutive model is greatly affected by the soft segment content, and the fitting effect is good when the soft segment content is high, while the fitting effect of the first-order Ogden model is bad. In addition, there is no effect when the drawing rate and shape change. This is because the first-order Ogden model can be simplified into Neo Hooken model and Mooney Rivlin model, which are suitable for the mechanical behavior of small deformation range and have poor fitting for the nonlinear large deformation process of the system.

Structural Analysis Using Applied Element Method: A Review

This paper presents a review on a displacement-based method of structural analysis. In Applied Element Method (AEM), the structure is simulated as an assembly of elements formed by dividing the structure virtually. These elements are connected in both normal and tangential directions by springs. AEM can be used to analyze structural behavior from the initial loading until total collapse. It combines between the advantages of Finite Element Method (FEM) and Discrete Element Method (DEM). In this paper, the differences between AEM and the other numerical methods are discussed. Next, basic introduction to AEM and its assumptions are presented. The element formulation and the effect of number of the connecting springs between elements in addition to the element size are illustrated. Finally, applications of AEM such as cyclic loading condition, dynamic small and large deformation range, creep theory, functionally graded material, masonry building and fiber reinforced polymer and polypropylene composite are explained.

A Modification on Applied Element Method for Linear Analysis of Structures in the Range of Small and Large Deformations Based on Energy Concept

In this paper, the formulation of a modified applied element method for linear analysis of structures in the range of small and large deformations is expressed. To calculate deformations in the structure, the minimum total potential energy principle is used. This method estimates the linear behavior of the structure in the range of small and large deformations, with a very good accuracy and low analytical time. The results show that analysis of a console beam by proposed method, even with minimum numbers of elements, in range of small deformations, has a computation error of less than 2%. Meanwhile, solving the same problem by Applied Element Method (AEM), has more than 31% error. Also, the buckling and post-buckling behavior of the structure, within the range of large deformations, is well-suited. So, with minimum number of elements, and very high accuracy, the buckling behavior of the fixed-base column was simulated. Also, the computational time of the proposed method is less than 40 percent of the computational time in the application of the applied elements method with 10 series of connection springs.

Zastosowanie piezoelementów typu bender do oceny sztywności początkowej gruntu nienasyconego z kontrolowanym ciśnieniem ssania

W artykule podjęto próbę oceny wpływu stopnia nasycenia gruntu wodą na jego sztywność w zakresie małych odkształceń. Właściwa analiza interakcji konstrukcji budowlanej z gruntem przeprowadzana z wykorzystaniem metod numerycznych wymaga znajomości parametrów, w szczególności charakterystyk sztywności w zakresie odkształceń odpowiadających rzeczywistym warunkom pracy tej konstrukcji. Zazwyczaj odkształcenia podłoża gruntowego wywołane obciążeniem od budowli nie przekraczają wartości 10–3, w związku z czym szczególnie ważne dla inżyniera geotechnika jest określenie sztywności gruntu w zakresie odkształceń 10–5–10–3. W celu wyznaczenia charakterystyk sztywności gruntu spoistego wykorzystano aparat trójosiowego ściskania wyposażony w piezoelementy typu bender, umożliwiające pomiar prędkości fali poprzecznej wewnątrz próbki. Podstawa opisywanego aparatu trójosiowego jest wyposażona w ceramikę o wysokim ciśnieniu wejścia powietrza (HAEV), co pozwoliło, wykorzystując technikę „translacji osi”, wykonać badania dla zmiennego (kontrolowanego) stopnia nasycenia próbki gruntu wodą. W literaturze stopień nasycenia (Sr) i wilgotność gruntu są wymieniane jako jedne z wielu czynników, które obok właściwości fizycznych, wartości naprężeń efektywnych, wskaźnika porowatości, historii naprężenia i innych wpływają na prędkość propagacji fali w gruncie. W publikacji opisano metodykę badań oraz przedstawiono wyniki badań własnych.

A generic approach to modelling flexible confined boundary conditions in SPH and its application

SummaryIn this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free‐surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto‐plastic computations of geomaterials, a robust numerical procedure to implement Mohr‐Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr‐Coulomb model. The proposed approach was first validated against two‐dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three‐dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.

Tensile and bending behavior of thin-walled triaxial weave fabric composites

The laminate model of thin-walled triaxial weave fabric composites (hereinafter referred to as shell-membrane structure) to calculate the equivalent tensile Young’s modulus and bending stiffness is derived. Three-dimensional beam element finite element model of shell-membrane structure under different loading angles is established, and the tensile and bending properties of shell-membrane structure were simulated, respectively. Both results of laminate model and three-dimensional beam element finite element model verify the “size effect,” indicating that the shell-membrane structure can be equivalent to linear material in the small deformation range. And the shell-membrane structure exhibits an in-plane quasi-isotropic property. These two methods are convenient for the mechanical properties solving in engineering applications.

Investigations in the field of material mechanics using strain gages

AbstractIn this contribution, investigations of the stress‐strain behavior of different metals using strain gage technique are presented. The measurement of strains using strain gages provides high measuring accuracy. In case of large deformations, the nonlinearity of the resistance‐strain‐relation, including elastic and plastic strain of the gage grid material, has to be considered. Moreover, for the detection of large deformations, high‐elongation strain gages and special bonding adhesives are used. Furthermore, at larger resistance changes the nonlinearity of the Wheatstone bridge has to be taken into account. As an example, the stress‐strain behavior of the steel 50CrV4 with 3 different process states in the small deformation range during tensile tests is demonstrated. The differences of the resulting stress‐strain curves of the material in the different process states are analyzed. Additionally, specimens of the aluminum alloy EN AW‐2024 are investigated in a large deformation range using tensile tests. Therein, the strain transmission enabled by the bonding is in the special focus. Furthermore, results of the large deformation tests are compared to the strain measurement using Digital Image Correlation.

Wyznaczanie maksymalnego modułu ścinania popiołów składowanych na składowisku mokrym

The design of above-ground ash storage sites requires an assessment of the safety performance of the structure (GEO). This is usually done by using finite elements methods, for which the geotechnical parameters measured in the range of small deformations should be provided. The paper compares the results of the maximum shear modulus obtained on the basis of laboratory and field tests. This parameter is derived from the theory of elasticity and is a measure of the material’s reaction to external loads in the range of small deformations (10–6–10–3%). The analysis of the results assumes that the range of low deformations corresponds to the response of the soil to the applied external loads. The paper presents the dependence of the maximum shear modulus on the effective stress and void ratio obtained on the basis of tests in a triaxial cell with piezoelectric elements. To determine Gmax in situ, SASW/CSWS methods were used to measure the velocity of acoustic waves generated from the ground surface. The authors’ many years of experience prove that determining the parameters of stiffness of a medium in the range of small deformations is essential for assessing the behavior of the material under the influence of stress changes. Ash stored in the form of post-bonded suspension has a high shear strength and the results of small strain stiffness tests should form the basis for determining the parameters for numerical methods for resistance and stability calculations.

High-Performance Strain Sensors Based on Spirally Structured Composites with Carbon Black, Chitin Nanocrystals, and Natural Rubber

In this research, a new type of conductive composite with high tensile strength, high elasticity, and cost competitiveness has been developed through solution mixing–spraying–rolling methods. Naturel rubber (NR) latex with chitin nanocrystals (ChNCs) as reinforcing filler and carbon black (CB) are thermally sprayed on glass substrate layer by layer, and then, spirally structured conductive composites are obtained by rolling the sheets. When the CB content is 4.44%, the conductivity of the NR/ChNCs-CB composite can reach 6.92 s/m. The tensile strength of 5% ChNCs reinforced conductive composites is 3.47 MPa, which is 3.1 times that of NR-CB composites without ChNCs. The strain sensor exhibits a high gauge factor (GF ≈ 5) and electrical conductivity stability in a small deformation range and still shows good stability and recoverability upon 25%, 50%, and 100% strain. The high-sensitivity strain sensors are further employed for monitoring human activities such as finger movements and pronunciation, which sh...

Logarithmic rate implementation in constitutive relations of finite elastoplasticity with kinematic hardening

AbstractThe objective of this article is the evaluation of the validity range of two objective rates, the nowadays most frequently used Jaumann rate and the recently introduced logarithmic rate, in material behaviour prediction due to large deformations. For that purpose the model subjected to large monotonic uniaxial elastoplastic deformation has been examined as well as the initially prestressed models which are afterwards exposed to the cyclic process of combined elastic lengthening and shearing. It is shown that whenever the participation of shear deformation to the total deformation stays in the small deformation range both rates are almost equal in constitutive relations implementation since the outputs for both rates are nearly congruent. Otherwise, if the influence of rotations is significant the Jaumann rate gives theoretically and experimentally unexpected results whereas the logarithmic rate results are stable and consistent with the notion of elasticity, i.e. without any residual stresses at the end of the elastic deformation cycles.

Numerical simulation of mechanical deformation of semi-solid material using a level-set based finite element method

In this work, a level-set based finite element method was used to numerically evaluate the mechanical behavior in a small deformation range of semi-solid materials with different microstructure configurations. For this purpose, a finite element model of the semi-solid phase was built based on Voronoï diagram. Interfaces between the solid and the liquid phases were implicitly described by level-set functions coupled to an anisotropic meshing technique. The liquid phase was considered as a Newtonian fluid, whereas the behavior of the solid phase was described by a viscoplastic law. Simulations were performed to study the effect of different parameters such as solid phase fraction and solid bridging. Results show that the macroscopic mechanical behavior of semi-solid material strongly depends on the solid fraction and the local microstructure which play important roles in the formation of hot tearing. These results could provide valuable information for the processing of semi-solid materials.

Deformation characteristics of flexible PU-coated multi-axial warp knitted fabrics under uniaxial tensile

Based on the characteristics of high tenacity, low density, flexible design, the coated fabric has emerged as a promising construct for tensile test. Here, it reports the deformation mechanism of a PU-coated multi-axial warp-knitted fabric under uniaxial tensile via a digital image correlation system. Specimens produced by us are chase in three fibre-reinforced directions namely 0°, 45° and 90°, respectively. The result shows that the crease does not have an effect on the deformations in the small deformation range (strain < 5%), and the deformation was evidently occurred near the fixed end lags because of the faster movement of specimen at the loading end, and the transverse shrinking at the edges is faster than that in the middle of the specimen. In the large deformation range, the strain fields are inconsistent at the same displacement revealing that the deformations of this kind of flexible coated fabric is in-homogeneous under tensile.

Study on Progressive Collapse Behavior of SRC Column-Steel Beam Hybrid Frame Based on Pushdown Analysis

To investigate the progressive collapse behavior of Steel Reinforced Concrete (SRC) column-steel beam hybrid frame after the failure of key structural elements, a PQ-Fiber model for an 8-storey structure is established in ABAQUS program. Nonlinear dynamic and static pushdown analysis are carried out after the failure and removal of the bottom-middle and bottom-corner columns. Numerical results of both methods agree well with each other. Results show that SRC column-steel frame has good resistance to progressive collapse under dynamic instantaneous load. After sudden removal of a bottom middle column, the development of structural collapse exhibits two mechanisms, the beam mechanism and the catenary mechanism. When the structure is within small deformation range, the collapse resistance of the residual frame is provided by the beam bending moment capacity, which is beam mechanism. For large deformation situation, the collapse resistance is mainly provided by the beam tensile strength, which is catenary mechanism. However, with the removal of a bottom corner column, the residual structure only undergoes the beam mechanism even for large deformations. For future practical applications, the influence of the steel ratio, steel section size, and the vertical position of the removed key components are investigated through a detailed parametric study.

Contact Analysis of Silicone Rubber Rectangular Ring in the Automatic Tighten Assembly

According to the uniaxial tension model and coulomb friction theory, by considering the nonlinear mechanical properties of rubber, the effect of deformation quantities of silicone rubber rectangular sealing ring on the assembly torque in tightening assembly process is researched in this paper. A stress-strain numerical model of silicone rubber rectangular sealing ring in small deformation range is established when tightening, on this basis, the numerical model is derived in deformation quantities of rectangular ring and assembly torque. Then having the torque-angle experiments by automatic tightening machine. The results show that, compared with the practical engineering experiment, the numerical model that reveals the relationship between the deformation quantities of the rectangular sealing ring and Assembly torque can reflect the effect of deformation on the assembly torque during the actual assembly process with great accuracy, which has a great reference value for the automatic assembly.

Identification of a Segment of the Yield Surface of a Two-Layer Pa38/M2R Composite

The aim of this study was to identify the initial yield surface of a two-layer aluminum alloy-copper composite in the range of small elastic-plastic deformations. Experimental tests in a plane stress state were conducted by loading tubular composite specimens with various combinations of axial forces and torque. The metal layers were joined together by using an epoxy resin. Independent studies were carried out for component of the composite under identical conditions. The yield surfaces obtained were compared with those given by the Huber–von Mises–Hencky and Tresca–Guest yield criteria. The yield criterion for the tested composite found by using a modified form of the rule of mixtures is presented. The yield surfaces of a Pa38/M2R composite and its components demonstrated the isotropic hardening.