Статті в журналах: "PLANE STRAIN CONDITION"

1

Nath, S. K. Deb. "Analytical Solution of Mixed Boundary Value Problems Using the Displacement Potential Approach for the Case of Plane Stress and Plane Strain Conditions." International Journal of Applied Mechanics and Engineering 22, no. 2 (May 24, 2017): 269–91. http://dx.doi.org/10.1515/ijame-2017-0016.

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AbstractTwo elastic plate problems made of duralumin are solved analytically using the displacement potential approach for the case of plane strain and plane stress conditions. Firstly, a one end fixed plate is considered in which the rest of the edges are stiffened and a uniform load is applied to the opposite end of the fixed end. Secondly, a plate is considered in which all of the edges are stiffened and a uniform tension is applied at its both ends. Solutions to both of the problems are presented for the case of plane stress and plane strain conditions. The effects of plane stress and plane strain conditions on the solutions are explained. In the case of stiffening of the edges of the plate, the shape of the plate does not change abruptly, which is clearly observed in both of the cases. For the plane strain condition, the plates become stiffer in the loading direction as compared to the plane stress condition. For the plane strain condition, there is a significant variation of the normal stress component, σzzat different sections of the plate. The graphical results, clearly identify the critical regions of the plate for the case of the plane stress and plane strain condition.

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2

Bukhanko, A. A. "PLASTICITY CONDITION CONNECTED WITH LEVEL LINES OF STRAIN STATE SURFACE FOR DIFFERENT DEFORMATION PROCESSES." Vestnik of Samara University. Natural Science Series 19, no. 9.2 (June 6, 2017): 43–54. http://dx.doi.org/10.18287/2541-7525-2013-19-9.2-43-54.

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On the basis of the theory of plastic flow the peculiarities of application of plasticity condition connected with level lines of strain state surface for work-hardening incompressible rigid-plastic body at different stressed states realized in the context of plane and axisymmetric strain, plane stressed state are considered. Comparison of the proposed condition with plasticity conditions of Mises and Tresca is carried out on the basis of construction of yield curves in deviatoric plane and in planes corresponding to certain stressed states. It is shown that the proposed plasticity condition describes plastic flow on the edge of Tresca prism in conditions of axisymmetric deformation.

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3

Cwiekala, Nils, Heinrich Traphöner, Peter Haupt, Till Clausmeyer, and A. Erman Tekkaya. "Analytical model of the in-plane torsion test." Acta Mechanica 233, no. 2 (January 24, 2022): 641–63. http://dx.doi.org/10.1007/s00707-021-03129-8.

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AbstractIn research and industry, the in-plane torsion test is applied to investigate the material behaviour at large plastic strains: a sheet is clamped in two concentric circles, the boundaries are twisted against each other applying a torque, and simple shear of the material arises. This deformation is analysed within the scope of finite elasto-plasticity. An additive decomposition of the Almansi strain tensor is derived, valid as an approximation for arbitrary large plastic strains and sufficiently small elastic strains and rotations. Constitutive assumptions are the von Mises yield criterion, an associative flow rule, isotropic hardening, and a physically linear elasticity relation. The incremental formulation of the elasticity relation applies covariant Oldroyd derivatives of the stress and the strain tensors. The assumptions combined with equilibrium conditions lead to evolution equations for the distribution of stresses and accumulated plastic strain. The nonzero circumferential stress must be determined from the equilibrium condition because no deformation is present in tangential direction. As a result, a differential-algebraic-equation (DAE) system is derived, consisting of three ordinary differential equations combined with one algebraic side condition. As an example material, properties of a dual phase steel DP600 are analysed numerically at an accumulated plastic strain of 3.0. Radial normal stresses of 3.1% and tangential normal stresses of 1.0% of the shear stresses are determined. The influence of the additional normal stresses on the determination of the flow curve is 0.024%, which is negligibly small in comparison with other experimental influences and measurement accuracies affecting the experimental flow curve determination.

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4

NAGASHIMA, Nobuo, and Masao HAYAKAWA. "Strain Distribution Measurement of a Crack Tip under a Plane Strain Condition." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A 79, no. 797 (2013): 23–33. http://dx.doi.org/10.1299/kikaia.79.23.

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5

Wanatowski, Dariusz, Jian Chu, and Wai Lay Loke. "Drained instability of sand in plane strain." Canadian Geotechnical Journal 47, no. 4 (April 2010): 400–412. http://dx.doi.org/10.1139/t09-111.

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Flowslide or failure of loose granular soil slopes is often explained using liquefaction or instability data obtained from undrained triaxial tests. However, under static loading conditions, the assumption of an undrained condition is not realistic for sand, particularly clean sand. Case studies have indicated that instability of granular soil can occur under essentially drained conditions (e.g., the Wachusett Dam failure in 1907). Laboratory studies on Changi sand by Chu et al. in 2003 have shown that sand can become unstable under completely drained conditions. However, these studies were carried out under axisymmetric conditions and thus, cannot be applied directly to the analysis of slope failures. In this paper, experimental data obtained from plane-strain tests are presented to study the instability behaviour of loose and dense sand under plane-strain conditions. Based on these test data, the conditions for the occurrence of drained instability in plane strain are established. Using the modified state parameter, the conditions for instability under both axisymmetric and plane-strain conditions can be unified. A framework for interpreting the instability conditions of sandy slopes developed under axisymmetric conditions also extends into plane-strain conditions.

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6

Teranishi, T., and Hironobu Nisitani. "Effectiveness of Non-Linear Crack Mechanics under Plane Strain Conditions." Key Engineering Materials 348-349 (September 2007): 497–500. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.497.

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The non-linear crack mechanics (NLCM) is a concept assuring the occurrence of the same phenomena in two cracked bodies under large scale yielding. It has been recognized that NLCM is effective in the cases of plane stress conditions. In this study, it was made clear that NLCM is effective not only in the case of plane stress condition but also in the case of plane strain condition.

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7

Niu, Hong Tao. "Simulation Method of Tunnel Excavation under Plane Strain Condition." Applied Mechanics and Materials 170-173 (May 2012): 1753–56. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.1753.

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For a different supporting time hole into subway tunnel excavation, with the initial stress in the surrounding rock in the tunnel and initial stress reverse impose the same release the equivalent of the simulation node, consider themselves lining load conditions in a hole under the formation of linear elastic numerical solution. The analysis indicated that with the increasing of the stress release rate, the hole arch displacement gradually decrease. When the stress release rate is bigger than a value, the hole arch displacement is increase rapidly, this is a marginal value (the biggest permission release rate); Under the identical hole diameter condition, the burying depth is bigger, the biggest permission release rate is bigger; Under the identical burying depth condition, the hole diameter is bigger, the biggest permission release rate is smaller.

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8

Galyautdinov, Z. R. "DYNAMIC STRENGTH CONDITION OF CONCRETE UNDER PLANE STRESS STATE." Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture 21, no. 4 (August 28, 2019): 138–45. http://dx.doi.org/10.31675/1607-1859-2019-21-4-138-145.

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Modern calculation models must take into account the dynamic deformation of reinforced concrete. Currently, the main regularities of nonlinear dynamic deformation of reinforced concrete under uniaxial stress state are theoretically analyzed in detail along with a wide range of experimental studies. Properties of concrete under plane stress -strain state and dynamic loading are examined to a lesser extent. This paper proposes the dynamic strength condition for the concrete strength which allows for changing the strain -hardening coefficient of concrete depending on the type of stress -strain state, the ratio of the primary stresses and the deformation rate.

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9

Dudko, Olga V., and Alexandr A. Mantsybora. "Shock Loading of Heteromodular Elastic Materials under Plane-Strain Condition." Key Engineering Materials 887 (May 2021): 634–39. http://dx.doi.org/10.4028/www.scientific.net/kem.887.634.

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The paper discusses the results of mathematical modeling the two-dimensional nonlinear dynamics of heteromodular elastic materials. The resistance of these materials under tension and compression is various. The deformation properties of the heteromodular medium are described within the framework of the isotropic elasticity theory with stress-dependent elastic moduli. In the plane strain case, it is shown that only two types of the nonlinear deformation waves can appear in the heteromodular elastic materials: a plane-polarized quasi-longitudinal wave and a plane-polarized quasi-transverse wave. Basing on obtained properties of the plane shock waves, two plane self-similar boundary value problems are formulated and solved.

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10

Wu, Qi, Yingjie Zhao, Norimasa Yoshimoto, Jinan Guan, Yukio Nakata, Shintaro Kajiyama, and Masayuki Hyodo. "Strain Rate-Dependent Mechanical Response of Hydrate-Bearing Sediments under Plane Strain Condition." Journal of Marine Science and Engineering 11, no. 6 (June 1, 2023): 1161. http://dx.doi.org/10.3390/jmse11061161.

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Natural gas hydrate has gained significant attention in recent years. To safely and sustainably exploit the natural gas from gas hydrate-bearing sediments, it is crucial to understand the long-term mechanical characteristics of the hydrate reservoir. In this study, the influence of hydrate and fine particles on the strain rate dependence of hydrate-bearing sediments under plane strain conditions has been studied. The experimental results show that the strain rate dependency of the mechanical properties of hydrate-bearing sediments is positively correlated with hydrate saturation instead of the morphology of hydrate in sediments. The residual strength of hydrate-bearing sediments is primarily controlled by the hydrate saturation and is independent of the strain rate. Changes in hydrate saturation and fines content can affect the relationship between the strain rate and shear band angle. Finally, the local volumetric expansion effect of hydrate-bearing sediments without fines content is more significant and shows a strong strain rate dependence characteristic. Overall, this study provides valuable insights into the long-term mechanical characteristics of hydrate reservoirs. These insights can contribute to the development of a constitutive model of hydrate-bearing sediments with time dependence in the future, which is meaningful to the exploitation of natural gas hydrate.

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11

Jong, Yong-Gwang, Yang Liu, Zixuan Chen, and Pieride Mabe Fogang. "Hypoplastic Interface Model considering Plane Strain Condition and Surface Roughness." Advances in Civil Engineering 2021 (August 30, 2021): 1–13. http://dx.doi.org/10.1155/2021/1473181.

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The soil-structure interface problem is an important part of soil-structure interaction research. These problems are mostly three-dimensional space problems, which is more complex to solve. In this paper, reduced stress and strain rate vectors are incorporated into the explicitly granular hypoplastic model by considering the plane strain state precisely. In addition, considering the important influence of roughness on the mechanical properties of contact surface, an improved hypoplastic model is established by incorporating the influence of roughness into the hypoplastic model, and the applicability of the new improved model is validated by comparing with the simulation results of the Mohr–Coulomb model, the explicitly granular hypoplastic models, and the experimental data. The results indicate that the improved model can be utilized to reflect the nonlinearity of the mechanical properties of the contact surface, which is in good agreement with the experimental data.

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12

Meknassi, Raid Fekhreddine, Gábor Béres, and Zsolt Lukács. "Optimization of notched tensile test specimen under plane strain condition." Multidiszciplináris tudományok 12, no. 3 (2022): 117–26. http://dx.doi.org/10.35925/j.multi.2022.3.11.

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In the current paper, specimen notch geometries during plane strain tensile test for cold-rolled steel DC01 is studied and optimized using Response Surface Methodology (RSM) and the desirability approach. The notch angle (X°), notch width (d), and notch length (c) were the main geometry parameters considered in this study. The effects of these parameters on the strain state were expressed by self-defined metrics, namely the Plane Strain State Index (PSSI) and the Homogeneity Index (HI) as well as those were analyzed by ANOVA analysis. The quadratic mathematical models obtained by the RSM presenting the evolution of the PSSI and the HI depending on (X°, d, and c) are presented. Optimization of the geometry parameters to achieve the optimal PSSI and better HI was carried out by a desirability function.

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13

Taendl, Johannes, Martina Dikovits, and Cecilia Poletti. "Investigation of the Hot Deformation Behavior of an Al-Mg-Sc-Zr Alloy under Plane Strain Condition." Key Engineering Materials 611-612 (May 2014): 76–83. http://dx.doi.org/10.4028/www.scientific.net/kem.611-612.76.

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This study investigates the hot deformation behavior of a new Al-Mg-Sc-Zr alloy under plane strain conditions. Flow curves corrected for deformation heating were calculated for strain rates between 0.01 and 10s-1 in a temperature range of 200 to 400°C. To evaluate the deformation behavior, strain rate sensitivity as well as flow localization parameter maps were calculated for strains of 0.2, 0.4, and 0.6. In addition, microstructural investigations and hardness measurements were performed for selected samples. It was shown that the flow stress decreased with deacreasing strain rate and increasing temperature. The best formability was observed for high strain rates and low temperatures as well as for low strain rates and high temperatures. In these cases no flow instabilities were observed.

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14

Lu, S. C.-Y., and P. K. Wright. "Finite Element Modeling of Plane-Strain Strip Drawing With Interface Friction." Journal of Engineering for Industry 110, no. 2 (May 1, 1988): 101–10. http://dx.doi.org/10.1115/1.3187857.

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Numerical results of plane-strain strip drawing are presented emphasizing the interfacial friction conditions between workmaterial and drawing die. The results are based on a large-strain elasto-plastic finite element code with a special boundary condition capability to treat interface friction. Two different modeling approaches are developed. In the interface velocity model, finite element solutions are based on the velocity boundary conditions along the die-work interface measured through transparent sapphire dies. In the interface traction model, a technique called “General Linear Boundary Condition,” is developed to incorporate many different existing friction models. Predicted values of drawing force, die separating force, global friction, and residual stresses from both models are favorably compared with the corresponding experimental measurements.

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15

Ma, Lin. "The Comparison of the Loess Mechanical Properties under Plane Strain and Conventional Triaxial Experiments." Advanced Materials Research 919-921 (April 2014): 791–94. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.791.

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Plane strain problem is currently prevalent in the loess engineering. However, this problem still using conventional triaxial test method for processing. So the paper conducted the plain strain test, analyze differences in plane strain experiments with conventional triaxial experiments under different moisture content and confining pressure. Research shows two points, the first one is the impact on the strength of the soil is more under moisture content than confining pressure, the other is that the soil strength under the plane strain condition is significantly greater than conventional triaxial conditions. It shows that the results were conservative under the plane strain problem at past. It played a certain role in guiding the engineering.

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16

Zhu, Xuli, Shanshan Ma, Haidong Huang, Xiaodong Wang, and Guirong Teng. "Displacement Analysis on Plane Stress Problems." Journal of Physics: Conference Series 2285, no. 1 (June 1, 2022): 012031. http://dx.doi.org/10.1088/1742-6596/2285/1/012031.

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Abstract The vertical z direction displacement component and its effect are not considered in the displacement analysis of the plane stress problems currently, and it may cause misunderstanding of the problems. The plane stress problems are three-dimensional problems actually because the strains are three-dimensional. The relationships among stress, strain and displacement of plane stress problems were analyzed in three-dimensional space based on the basic theory of elasticity in this paper. According to the characteristic constraints of the plane stress problems, the displacement expressions in three directions were derived. The displacement in the plane consists of the integral of the plane strain in the x-y plane and the independent function of the z-direction. Under the condition that the plane stress problem is strictly satisfied, the first stress invariant should be linearly distributed in the plane, and the displacement in the z direction is the product of the x, y related linear function and z.

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17

Liu, Ji Yuan, and Tai Quan Zhou. "Finite Element Analysis of Clay Shear Band under Plane Strain Condition." Applied Mechanics and Materials 638-640 (September 2014): 462–65. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.462.

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The clay shear band analysis under plane strain condition were based on modified cam clay model in finite element software ABAQUS. Normally Consolidated Clay and lightly overconsolidated clay were analyzed in the article. Loading speed, size of soil specimen, different consolidation state (Normally Consolidated Clay and lightly overconsolidated clay) are considered. These factors have effect on the distribution of Pore water pressure, the effective stress path of nodes in shear band and out of shear band and the angle between the shear band and horizontal line. All the differentia and effects were used to analyze the production conditions and formation mechanism of shear band. The results show that size of clay specimen can influence the number of shear band. When the height-width ratio is large, the number of shear band will increase.

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18

Dikshit, S. N. "Ballistic Behaviour of Tempered Steel Armour Plates under Plane Strain Condition ." Defence Science Journal 48, no. 2 (January 1, 1998): 167–72. http://dx.doi.org/10.14429/dsj.48.3896.

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19

Lu, De Chun, Xiu Li Du, An Nan Zhou, and Yang Ping Yao. "The Principal Stresses of Soil Mass in the Direction of Plane Strain." Advanced Materials Research 243-249 (May 2011): 2657–65. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.2657.

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The characteristics of deformation and strength of soils under the plane strain condition can be simplified as a two-dimensional problem. How to easily and reasonably determine the value of principal stress in the direction of plane strain is the key point. Based on the Elastic-plastic stress-strain relationship for soil and test data under the plane strain condition, it is assumed that the relationship between principal stresses in plain strain direction and the principal stresses in the other directions is bilinear. The parameters of bilinear function are determined by one-dimensional consolidation and failure state. The principal stress in plain strain direction is expressed as a function of stress states and material properties. Compared with test results, the rationality of the proposed bilinear principal stress function is testified.

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20

Šebek, František, Jindrich Petruška, and Petr Kubík. "Behavior of Lode Dependent Plasticity at Plane Strain Condition and its Implication to Ductile Fracture." Solid State Phenomena 258 (December 2016): 213–16. http://dx.doi.org/10.4028/www.scientific.net/ssp.258.213.

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Variety of metals are complex materials exhibiting various behavior under different loading. Many metallic materials exhibit Tresca-like behavior rather than von Mises. It means different behavior in tension under plane strain and uniaxial stress conditions. This might be described by Lode dependent plasticity which should result in better prediction in force or torque responses of material tests. Good agreement between computation and experiment is also very important when calibrating the ductile fracture criteria. Several tests under plane strain and uniaxial stress states were carried out on aluminum alloy 2024-T351 where the Lode dependency was significant. The Lode dependent plasticity was implemented along with von Mises and Tresca-like yield criteria, which resulted in improvement of force–displacement responses of plane strain tests simulations. But it also caused significant change in the stress state of tensile flat and grooved plates which wrongly approached uniaxial tension condition. This inconvenience prevents plane strain experiments from using for calibration of ductile fracture criteria under these circumstances.

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21

Zou, Huiran, Weilong Yin, Chaocan Cai, Bing Wang, Ankang Liu, Zhen Yang, Yibin Li, and Xiaodong He. "The Out-of-Plane Compression Behavior of Cross-Ply AS4/PEEK Thermoplastic Composite Laminates at High Strain Rates." Materials 11, no. 11 (November 17, 2018): 2312. http://dx.doi.org/10.3390/ma11112312.

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The dynamic mechanical behavior of thermoplastic composites over a wide range of strain rates has become an important research topic for extreme environmental survivability in the fields of military protection, aircraft safety, and aerospace engineering. However, the dynamic compression response in the out-of-plane direction, which is one of the most important loading conditions resulting in the damage of composite materials, has not been investigated thoroughly when compared to in-plane compression and tensile behavior under high strain rates. Thus, we used split Hopkinson pressure bar (SHPB) tests to conduct the out-of-plane compression test of cross-ply carbon fiber-reinforced polyetheretherketone (AS4/PEEK) composite laminates. Afterward, the damage mechanism under different strain rates was characterized by the macrostructure morphologies and scanning electron microscope micrographs. Two major cases of the incomplete failure condition and complete failure condition were discussed. Dynamic stress-strain curves expound the strain rates dependencies of elastic modulus, failure strength, and failure strain. An obvious spring-back process could be observed under incomplete failure tests. For the complete failure tests, secondary loading could be observed by reconstructing and comparing the dynamic response history. Lastly, various failure modes that occurred in different loading strain rates illustrate that the damage mechanism also shows obvious strain rate sensitivity.

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22

Sathananthan, Iyathurai, and Buddhima Indraratna. "Plane-strain lateral consolidation with non-Darcian flow." Canadian Geotechnical Journal 43, no. 2 (February 1, 2006): 119–33. http://dx.doi.org/10.1139/t05-094.

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New plane-strain lateral consolidation equations are formulated that neglect the well resistance of vertical drains but are applicable for both Darcian and non-Darcian flow. The results of consolidation analyses using conventional Darcian (linear) flow and the new solution based on non-Darcian (exponential) flow are compared. A good match has been obtained between equivalent plane-strain and axisymmetric solutions. The advantage of the equivalent plane-strain procedure is that it not only matches the average degree of radial (axisymmetric) consolidation but also yields a more realistic excess pore pressure distribution in the lateral direction than the Darcian flow condition. The relevant parameters are illustrated graphically for convenience. Good agreement was obtained between the prediction of the new equivalent plane-strain solution and field data from a test area in Ska-Edeby, Sweden.Key words: plane strain, consolidation, soft clay, vertical drains.

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23

Sawant, V. A., and M. S. Norazzlina. "FLEXURAL STRESS ANALYSIS OF RIGID PAVEMENTS USING AXI-SYMMETRIC AND PLANE STRAIN FEM." ASEAN Journal on Science and Technology for Development 24, no. 4 (November 16, 2017): 443–51. http://dx.doi.org/10.29037/ajstd.218.

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The design of pavement involves a study of soils and paving materials, their response under load for different climatic conditions. In the present study, an attempt has been made to compare stresses predicted using two finite element analyses. First analysis is based on the twodimensional plane strain assumption where as in second approach axi-symmetric condition is assumed to consider three-dimensional behavior of rigid pavement. The results are compared with flexural stresses obtained from conventional Portland Cement Association method. The computed flexural stresses obtained from axi-symmetric condition are found to be in close agreement with PCA method. Results of plane strain analysis show a fair agreement after application of an appropriate multiplication factor

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24

Xiang, Y., X. Chen, and J. J. Vlassak. "Plane-strain Bulge Test for Thin Films." Journal of Materials Research 20, no. 9 (September 2005): 2360–70. http://dx.doi.org/10.1557/jmr.2005.0313.

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The plane-strain bulge test is a powerful new technique for measuring the mechanical properties of thin films. In this technique, the stress–strain curve of a thin film is determined from the pressure-deflection behavior of a long rectangular membrane made of the film of interest. For a thin membrane in a state of plane strain, film stress and stain are distributed uniformly across the membrane width, and simple analytical formulae for stress and strain can be established. This makes the plane-strain bulge test ideal for studying the mechanical behavior of thin films in both the elastic and plastic regimes. Finite element analysis confirms that the plane-strain condition holds for rectangular membranes with aspect ratios greater than 4 and that the simple formulae are highly accurate for materials with strain-hardening exponents ranging from 0 to 0.5. The residual stress in the film mainly affects the elastic deflection of the membrane and changes the initial point of yield in the plane-strain stress–strain curve, but has little or no effect on further plastic deformation. The effect of the residual stress can be eliminated by converting the plane-strain curve into the equivalent uniaxial stress–strain relationship using effective stress and strain. As an example, the technique was applied to an electroplated Cu film. Si micromachining was used to fabricate freestanding Cu membranes. Typical experimental results for the Cu film are presented. The data analysis is in good agreement with finite element calculations.

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25

Park, Namsu, and Hoon Huh. "Prediction of Fracture Strains for DP980 Steel Sheets Using a Modified Lou–Huh Ductile Fracture Criterion." Key Engineering Materials 626 (August 2014): 347–52. http://dx.doi.org/10.4028/www.scientific.net/kem.626.347.

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This paper is concerned with the prediction of fracture strains for DP980 steel sheets using a modified Lou–Huh ductile fracture criterion. The usage of DP980 steel is significantly increasing in the automotive industry for weight reduction, enhancement of crashworthiness and safety of car body. The material behavior of AHSS show unpredictable and sudden fracture during sheet metal forming process. A modified Lou–Huh ductile fracture criterion is utilized to predict the formability of AHSS because the conventional FLD constructed based on necking is unable to evaluate the formability of AHSS. Fracture loci were extracted from 3D fracture envelopes by assuming the plane stress condition to evaluate equivalent plastic strain up to the point of fracture at a wide range of loading paths. Three different types of specimens such as pure shear, dog-bone and plane strain grooved specimens were used for tensile tests to construct 3D fracture envelopes of DP980. Fracture strain of each loading path was evaluated to show that there is little deviation between predicted fracture strains and experimentally acquired ones. From the comparison, it is concluded that the 3D fracture envelopes can accurately predict the onset of the fracture of DP980 steel sheets in complicated loading conditions including the pure shear condition.

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26

Djavid, M. "Particle Orientation and Velocity Equations of Clay in a Plane-Strain Condition." Journal of Applied Mechanics 62, no. 1 (March 1, 1995): 126–30. http://dx.doi.org/10.1115/1.2895892.

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The directional property of soils, particularly clays, are directly related to the particle orientations. The platy clay particles do possess the tendency to reorient themselves in the most stable condition against applied stress. One may conceive of developing a soil model directly relating particle orientation and applied stress. In this study an angle θ, which is the preferred (therefore stable) orientation of clay particles, is introduced. Using this concept and slip-line theory, the velocity equations of clay in a plane-strain condition are developed. In this approach any change in clay particle orientation is essentially dependent on principal stresses magnitudes as well as their directions. Therefore, the effect of rotation of principal stresses can be included and quantified.

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27

Wang, J. F., and H. B. Yan. "3D DEM Simulation of Crushable Granular Soils under Plane Strain Compression Condition." Procedia Engineering 14 (2011): 1713–20. http://dx.doi.org/10.1016/j.proeng.2011.07.215.

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28

Elsworth, D. "Wedge stability in the roof of a circular tunnel: Plane strain condition." International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 23, no. 2 (April 1986): 177–81. http://dx.doi.org/10.1016/0148-9062(86)90345-1.

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29

Surendran, C. S., and G. Sasikala. "Representation of Damage with Fracture-Strain." Applied Mechanics and Materials 592-594 (July 2014): 1205–9. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.1205.

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Under the influence of stresses and strains damage is progressively accumulated in the material leading to full damage viz. fracture corresponding to a critical damage parameter. The damage parameter varies in between zero and unity inclusive of both the values corresponding to non damaged and fully damaged condition. Also damage is a tensorial quantity with physical meaning. In order to represent this physical quantity, a damage-D plane is suggested. This is like a co-ordinate system to easy representation of damage as a function of fracture strain. The damage-D plane can be merged with engineering stress-strain curve beyond the UTS where the damage leads to fracture occurs in the material.

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30

Zhang, Zhen, Fengrui Rao, Guanbao Ye, and Jiangting Liu. "Mechanical Performance and Void Structure Change of Foamed Cement Paste Subjected to Static and Cyclic Loading under Plane Strain Conditions." Materials 15, no. 5 (February 24, 2022): 1711. http://dx.doi.org/10.3390/ma15051711.

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Cement-based lightweight materials have received much attention recently in embankment backfill applications, the boundary of which is more close to a plane strain condition. To study the influence of plane strain condition on the behavior and void structure of cement-based lightweight material under cyclic loading, this paper conducted a series of compression tests on foamed cement pastes with densities of 700 and 900 kg/m3 subjected to static and cyclic loading under plane strain conditions. The X-CT technique was adopted to obtain the three-dimensional (3-D) void structures of the specimens before and after the loading tests. The results showed that the plane strain conditions yielded specimen compression strengths 30–50% higher than the unconfined conditions. The specimen integrity endured under load levels of less than 0.5, but failed after approximately 1000 cycles under a load level of 0.8, indicating that cyclic loading could accelerate the degradation of the specimena. The void structures of the specimens showed that the void volumes were featured bfatured an unimodal distribution with unimodal positions in a range of 0.1–0.2 mm3. The unimodal position became higher with the increasing cyclic load level. Slices of the specimens after static and cyclic loading tests suggested that cyclic load could easily lead to the rupture of voids that then merge into bigger voids and the connection of voids forming cracks.

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31

Alaca, B. Erdem, K. Bugra Toga, Orhan Akar, and Tayfun Akin. "Strain-controlled bulge test." Journal of Materials Research 23, no. 12 (December 2008): 3295–302. http://dx.doi.org/10.1557/jmr.2008.0395.

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A closed-loop approach is adopted to implement strain rate control during the bulge test. Due to the difficulty of measuring strains directly, the technique is based on the conversion of displacement measurements to the corresponding strains using the plane-strain formulation. The necessary temporal evolution of the midpoint displacement of a rectangular diaphragm is derived under the condition of constant strain rate and is imposed as a control criterion. The technique is demonstrated on 500-nm-thick Au diaphragms by applying strain rates ranging from 2 × 10−6 to 2 × 10−4 s–1. By measuring the corresponding yield strength values, a strain rate sensitivity of 0.11 is obtained, which is close to what was previously reported on similar specimens using the microbending test.

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32

Liu, Yao He, Guo Feng Yi, and Jian Ming Xiong. "An Analytical Solution to Metal Plane Problem in Terms of Orthotropic Anisotropy and Strain Hardening." Advanced Materials Research 97-101 (March 2010): 348–56. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.348.

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In this paper, the yield condition of Hill’s orthotropic yield criterion under axial symmetric plane stress state was discussed. The yield function of orthotropic material was proposed and the analytical solution to meet the condition of equations of equilibrium and compatibility under axial symmetric plane stress state is obtained, in which the conditions of power hardening materials was considered. The research result indicates that hardening coefficient and anisotropic parameter have substantial influence over stress and strain. However, in the presence of the coefficient R90=H/F，the influence appears to be quite weak.

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33

Garagash, Dmitry I., and Emmanuel Detournay. "Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution." Journal of Applied Mechanics 72, no. 6 (April 10, 2005): 916–28. http://dx.doi.org/10.1115/1.2047596.

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The paper considers the problem of a plane-strain fluid-driven fracture propagating in an impermeable elastic solid, under condition of small (relative) solid toughness or high (relative) fracturing fluid viscosity. This condition typically applies in hydraulic fracturing treatments used to stimulate hydrocarbons-bearing rock layers, and in the transport of magma in the lithosphere. We show that for small values of a dimensionless toughness K, the solution outside of the immediate vicinity of the fracture tips is given to O(1) by the zero-toughness solution, which, if extended to the tips, is characterized by an opening varying as the (2∕3) power of the distance from the tip. This near tip behavior of the zero-toughness solution is incompatible with the Linear Elastic Fracture Mechanics (LEFM) tip asymptote characterized by an opening varying as the (1∕2) power of the distance from the tip, for any nonzero toughness. This gives rise to a LEFM boundary layer at the fracture tips where the influence of material toughness is localized. We establish the boundary layer solution and the condition of matching of the latter with the outer zero-toughness solution over a lengthscale intermediate to the boundary layer thickness and the fracture length. This matching condition, expressed as a smallness condition on K, and the corresponding structure of the overall solution ensures that the fracture propagates in the viscosity-dominated regime, i.e., that the solution away from the tip is approximately independent of toughness. The solution involving the next order correction in K to the outer zero-toughness solution yields the range of problem parameters corresponding to the viscosity-dominated regime.

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34

Ortner, Balder. "The Choice of Lattice Planes in X-Ray Strain Measurements of Single Crystals." Advances in X-ray Analysis 29 (1985): 113–18. http://dx.doi.org/10.1154/s0376030800010181.

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It is well known that all of the six independent components of the strain tensor can be calculated if the linear strains in six appropriate directions are known (e.g.). That calculation is to solve a system of linear equations, whose coefficients are defined by the orientations of the measured planes. The strains are determined by lattice plane distance measurements using X-rays.The linear equation system can only be solved if the matrix of coefficients has rank. Whether this condition is met or not can be decided without calculating a determinant just from geometric relationships among the planes to be measured. A demand beyond that necessary condition is to make the matrix of coefficients so that the accuracy of the calculated strain tensor is best. From error calculation we know that there exist distinct ratios between the inevitable measurement errors and the errors of the calculated strain components. These ratios depend strongly on the geometric relationship among the lattice planes. It is the purpose of this paper to show how lattice planes should be chosen in order to get these ratios as small as possible i.e. to get a maximum of accuracy at a given number of measurements, or a minimum of experimental effort if a distinct limit of error is to be reached.

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35

Wu, Ke, Ming Yue Ma, and Dong Xue Hao. "Study on Grouting Pressure of Splitting Grouting Based on Cylindrical Expansion Considering Large Strain." Advanced Materials Research 378-379 (October 2011): 288–91. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.288.

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Anti-seepage reinforcement technology of splitting grouting to improve the stability of dam, has been an effective reinforcement method in the field of dam reinforcement. Based on the extended SMP criterion and stress-dilatancy relation considering large strain, the governing equations of axisymmetric problem in the plane strain condition and the partial differential equations for the boundary-value problem of cavity expansion in frictional cohesive soils were established. Then, the early phase of splitting grouting is regarded as the plane strain question of cylindrical expansion infinite soil. Under initial grouting pressure, the soil body was supposed as ideal elastic mass. However, the soil body was supposed to generate plastic damage considering large strain with the increase of grouting pressure and submit the extended spatial mobilization plane theory. Solutions of radial and hoop stresses and strains around the grouting cavity were obtained by recursive computations. Furthermore, the influence of damage softening parameter, cohesion and friction angle was examined by a parametric study.

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36

Yang, Ping, Zude Zhao, Li Meng, Xueping Ren, and Shao Dong Huang. "Texture, Microstructure and Strain Sensibility in Compressed Magnesium Alloys." Materials Science Forum 488-489 (July 2005): 185–88. http://dx.doi.org/10.4028/www.scientific.net/msf.488-489.185.

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Depending on its initial texture and external strain condition differences in deformation mechanisms, kinetics of dynamic recrystallization or even superplastic behaviors may emerge in magnesium alloys leading to distinct microstructure and texture evolutions. When imposed strain condition is altered, e.g. from plane strain compression to rolling or uniaxial compression, the deformation anisotropy will decrease in different rates and basal slip and {1012} twinning will dominate deformation process. This work examines this strain sensibility by inspecting the σ-ε curves, microstructures and textures in a quasi plane-strain compressed ZK60 alloy and compares the results with those of AZ31 alloy compressed in channel die.

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37

Galkiewicz, Jaroslaw. "The Influence of In-Plane Constraint on Void Behavior in Front of a Crack in Plane Strain." Solid State Phenomena 224 (November 2014): 139–44. http://dx.doi.org/10.4028/www.scientific.net/ssp.224.139.

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This paper investigates voids’ behavior in front of a crack in elastic-plastic material under plane strain condition. Using the modified boundary layer approach for selected values of Q-stress it evaluates the deformations of a material cell. The deformations are recomputed with an exact three-dimensional model.

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38

KUWAMURA, Hitoshi, and Yuichiro INABA. "STRESS TRIAXIALITY AND STRAIN CONCENTRATION AT STEEL CONNECTIONS UNDER PLANE STRAIN CONDITION : Stress-strain states at steel connections-Part 1." Journal of Structural and Construction Engineering (Transactions of AIJ) 64, no. 518 (1999): 87–94. http://dx.doi.org/10.3130/aijs.64.87_1.

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39

Zha, Zhi Xiang, Wei Peng, and Xi La Liu. "Experimental and Numerical Simulation Study on the Shear Stress for the Interfaces of Anchorage Type Structures." Advanced Materials Research 163-167 (December 2010): 1325–28. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.1325.

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A laboratory test of anchor pull-out model under plane-strain condition on the shear stress transfer for the interfaces of anchorage type structures was carried out in this paper. The results of test were verified by corresponding numerical simulation model. It was proved that the pull-out experimental model under plane-strain condition was an effective model used to research the working mechanism of anchorage structure.

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40

Hsieh, Pio-Go, and Chang-Yu Ou. "Analysis of deep excavations in clay under the undrained and plane strain condition with small strain characteristics." Journal of the Chinese Institute of Engineers 35, no. 5 (July 2012): 601–16. http://dx.doi.org/10.1080/02533839.2012.679115.

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41

Santamarina, J. C., and G. Cascante. "Stress anisotropy and wave propagation: a micromechanical view." Canadian Geotechnical Journal 33, no. 5 (November 6, 1996): 770–82. http://dx.doi.org/10.1139/t96-102-323.

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Wave propagation is a constant-fabric macrophenomenon, suitable to microinterpretation. Both velocity and attenuation characterize state, including inherent and stress-induced anisotropy. The purpose of this research is to study the effect of isotropic and deviatoric stresses on wave propagation in particulate materials at low strains and to interpret results at the microlevel. A resonant-column device was midified to allow for the application of axial extension and axial compression deviatoric loading. The fixed-free boundary condition of the sample was maintained. Data for round, hard-grained sand show that shear wave velocity and attenuation are primarily dependent on the mean stress on the polarization plane, with minimal effect of the deviatoric component, in agreement with prior observations at stress ratios less than 23. Attenuation is strongly correlated with the mean stress in the polarization plane and the level of shear strain. Damping does not vanish at low strains, contrary to predictions based on hysteretic behaviour; hence, other loss mechanisms must take place at low strains. Low-strain wave parameters are adequately corrected for mid-strain using modified hyperbolic models. Measured velocity and damping trends during isotropic and anisotropic loading qualitatively agree with predictions based on regular arrays. Key words: mechanical waves, resonant column, damping, shear modulus, stress anisotropy, random vibration.

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42

Kim, Kwon Hoo, Jun Ho Choi, Kwang Il Hwang, Han Sang Kwon, Kazuto Okayasu, and Hiroshi Fukutomi. "Texture Formation Behaviors in AZ80 Magnesium Alloy during High-Temperature Plane Strain Compression." Advanced Materials Research 1110 (June 2015): 152–57. http://dx.doi.org/10.4028/www.scientific.net/amr.1110.152.

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The behavior of texture formation during high-temperature deformation in AZ80 magnesium alloy is investigated. Three kinds of specimens were machined out from rolled plates. The plane strain compression tests were conducted at various deformation conditions – temperature, strain and strain rate. After compression deformation, texture measurement was carried out on the mid-plane section parallel to the compression direction by the Schulz reflection method and EBSD measurement. The maximum values of the flow stress are observed in all the cases at the true stress – true strain curve for three type of specimens. It is found that the main component of texture and the accumulation of pole density vary depending on deformation condition and initial texture. Six kinds of crystal orientation components have been observed after deformation in total. (0001)<10-10> is formed regardless of the initial texture.

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43

Adams, M. J., B. J. Briscoe, G. M. Corfield, C. J. Lawrence, and T. D. Papathanasiou. "An Analysis of the Plane-Strain Compression of Viscoplastic Materials." Journal of Applied Mechanics 64, no. 2 (June 1, 1997): 420–24. http://dx.doi.org/10.1115/1.2787325.

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A theoretical analysis for the plane-strain compression of viscoplastic materials with a Tresca wall boundary condition is described. The analysis is based upon the incorporation of a viscoplastic associated flow rule into the cycloidal solution originally developed for rigid-perfectly plastic materials. The evolution of the calculated stress field suggests that the influence of strain rate hardening is similar to that reported previously for strain hardening. The calculated strain fields are elliptical in form and are consistent with those measured for a viscoplastic paste. Previous analyses of the compression of viscoplastic materials have employed the lubrication approximation for fluid flows with a resulting kinematic inconsistency in the predicted velocity fields.

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44

Bhat, Sunil, and C. Solaimuthu. "On Stress-Strain Fields near Mode i Ductile Crack Tip in Elastic-Plastic Fracture." Defect and Diffusion Forum 428 (August 22, 2023): 9–15. http://dx.doi.org/10.4028/p-qztrb0.

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A mode I, centre crack, in ductile steel plate of finite dimensions is modeled in ANSYS software. Non-linear stress-strain data of steel are used. Plane strain case is adopted. A suitable value of far field tensile stress (pressure) is chosen such that EPFM condition prevails at the crack tip. Process and plastic zones are obtained at the crack tip. Desired values are noted. Areas of high stress and high strain are identified. Validation of void nucleation taking place ahead of crack tip and not exactly at the crack tip and coalescence of voids happening at the crack tip are confirmed from the results. Plots between the distance of desired location from the crack tip and load line stresses and strains are drawn. The plots are in accordance with the expectations.

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45

Ress, D. W. A., and R. K. Power. "Orientation and formability of orthotropic sheet metals." Journal of Strain Analysis for Engineering Design 32, no. 1 (January 1, 1997): 61–81. http://dx.doi.org/10.1243/0309324971513229.

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This paper examines the formability of automotive sheet metals: CR steels and 6000 series aluminium-magnesium alloys. Necking strains are used to determine the forming limits; i.e. a diffuse instability condition is reached under in-plane biaxial stressing. The theory admits material anisotropy, work-hardening and sheet orientation under any ratio of applied principal stresses. It has been programmed to accept orientations between the principal stress axes and the sheets' rolling direction in 15° increments between 0° and 90°. The ratio between the principal stresses may vary between 0 and ± 1. The input data required are the width-thickness strain ratios ( r values) in directions 0°, 45° and 90° to the roll and the Hollomon hardening exponent ( n value). The output is presented in four diagrams: the critical subtangent-stress ratio and plots between three combinations of the limiting principal engineering strains: (a) two in-plane strains, (b) major in-plane strain versus thickness strain and (c) minor in-plane strain versus thickness strain. Each diagram shows the influence of rotating the principal stress axes in increments of 15° to the roll. The forming limit diagram of type (a) gives the traditional presentation of a forming limit diagram (FLD). This FLD may be established experimentally from the strain in a surface grid lying around splits. In practice, a few production panels may be gridded for die-tryout and to examine a change in material. The alternative FLDs, types (b) and (c), are proposed to provide quality control with the increasing use of ultrasonics to monitor thickness of pressed panels. An example of type (b) is determined experimentally for CR1 steel.

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46

Fernández Canteli, A., E. Giner, D. Fernández Zúñiga, and J. Fernández Sáez. "On the Path and Area J_x1-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates." Key Engineering Materials 417-418 (October 2009): 421–24. http://dx.doi.org/10.4028/www.scientific.net/kem.417-418.421.

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In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-plane dimensions. For thin plates, it is shown that the 2D plane stress condition is impossible in the close neighbourhood of a 3D crack front under elastic behaviour so that the consideration of an equivalent Young modulus E', used to find a simple relation between the J(s)-integral and KI for different constraint levels can be misleading.

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47

Lee, Seung-Hyun, and Byoung-Il Kim. "Analytical Study on Characteristics of von Mises Yield Criterion under Plane Strain Condition." Journal of the Korea Academia-Industrial cooperation Society 16, no. 9 (September 30, 2015): 6391–96. http://dx.doi.org/10.5762/kais.2015.16.9.6391.

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48

Chen, Z., M. Omidvar, and M. Iskander. "Observations of Multi-Scale Granular Kinematics Around Driven Piles in Plane Strain Condition." Geotechnical Testing Journal 39, no. 5 (May 30, 2016): 20150199. http://dx.doi.org/10.1520/gtj20150199.

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49

Tomita, Yoshihiro, and Youngsuk Kim. "Bifurcation behaviour of bilayered tubes subjected to uniform shrinkage under plane strain condition." International Journal of Solids and Structures 29, no. 22 (1992): 2723–33. http://dx.doi.org/10.1016/0020-7683(92)90114-9.

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50

Indraratna, Buddhima, M. Mahdi Biabani, and Sanjay Nimbalkar. "Behavior of Geocell-Reinforced Subballast Subjected to Cyclic Loading in Plane-Strain Condition." Journal of Geotechnical and Geoenvironmental Engineering 141, no. 1 (January 2015): 04014081. http://dx.doi.org/10.1061/(asce)gt.1943-5606.0001199.

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