A Constitutive Model for Saturated Gravelly Sand Based on Higher-Order Dilatancy Equation

A standard stress path triaxial test system was applied to carry out conventional triaxial shearing tests for gravelly sands under confining pressures ranging from 50 kPa to 400 kPa at the initial relative densities of 0.15, 0.35, 0.55, and 0.75, respectively. The test results show that all the samples of gravelly sand present strain hardening and shear contraction during the process of shearing test. Additionally, gravelly sands are significantly affected by the initial relative density. The hardening degree of gravelly sand samples rises in line with increasing initial relative densities during shearing tests. When initial relative densities Dr are at 0.15 and 0.35, the volume shrinkage of samples decreases with the increasing confining pressures. Instead, when initial relative densities Dr are at 0.55 and 0.75, the volume shrinkage of samples increases with the growth of confining pressures. To describe these triaxial shearing mechanical properties of gravelly sands, a higher-order dilatancy equation was proposed based on the concept of a super yield surface. A constitutive model which can describe the mechanical properties of gravelly sand was established when the associated flow laws were applied to compare with the results of the triaxial shearing test under the consolidated drained condition. The comparison results showed that the proposed model can reflect the strain hardening and shear contraction characteristics of gravelly sands from low to high confining pressures under different initial relative densities.

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Constitutive Model of N15 Propellant considering the Confining Pressure Effect

International Journal of Aerospace Engineering ◽

10.1155/2021/2661184 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Tianpeng Li ◽

Junli Han ◽

Shixin Wang ◽

Yong He ◽

Xiong Chen ◽

...

Keyword(s):

Mechanical Properties ◽

Constitutive Model ◽

Pressure Effect ◽

Rupture Strength ◽

Confining Pressure ◽

Test System ◽

Model Parameters ◽

Initial Modulus ◽

Confining Pressures ◽

Confining Pressure Effect

To describe the effect of confining pressure on the mechanical responses of N15 propellant, a constitutive model considering the confining pressure effect was first established for N15 propellant based on the elastic-viscoelastic correspondence principle. Then, the mechanical properties of N15 solid propellant under different confining pressures were obtained using confining pressure test system, and the obtained results indicate that the initial modulus of propellant did not change with confining pressure, but the maximum tensile strength, rupture strength, the maximum elongation, and elongation at break increased with increasing confining pressure. In conjunction with propellants’ mesoscopic structure and cross-section analysis, the mechanical mechanism of confining pressure effect on propellant was initially disclosed. Due to confining pressure, the particle dewetting inside the propellant was reduced, the hole propagation was delayed, and crack extension inhibited germination, proving that confining pressure has a strengthening impact on the propellant. Finally, assuming that the model parameters were dependent on pressure, the model parameters acquisition and validation were conducted. The results demonstrated that constitutive model can describe confining pressure influence on the mechanical properties of N15 propellant accurately.

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A Characteristic and a Precisely Constitutive Model for Undrained Clay

Materials Science Forum ◽

10.4028/www.scientific.net/msf.975.203 ◽

2020 ◽

Vol 975 ◽

pp. 203-207

Author(s):

Shih Tsung Hsu ◽

Wen Chi Hu ◽

Yu Heng Lin ◽

Zhuo Ling

Keyword(s):

Shear Strength ◽

Plastic Strain ◽

Constitutive Model ◽

Strain Hardening ◽

Undrained Shear Strength ◽

Triaxial Tests ◽

Stress Strain ◽

Proposed Model ◽

Taipei Basin ◽

Undrained Shear

Constitutive models for soils are usually adopted in numerical method to analyze the behavior of geotechnical structures. This study performs a series of consolidated-undrained triaxial tests to establish the stress-strain curve of clay. A constitutive model that considers continuous strain hardening-softening is proposed based on the results of triaxial tests. Triaxial test results reveal that undrained shear strength linearly increases with an increase in consolidated pressure , the normalized undrained shear strength is about 0.52 not only for this study but also for the other two cases around Taipei Basin. Due to undrained condition, an associated flow rule between plastic strain increment and stress tensor is adopted. As accumulative plastic strain or/and consolidated pressure change, the mobilized undrained shear strength also changes. All parameters needed for the proposed model can be expressed as a function of undrained shear strength Su, The mobilized undrained shear strength for the proposed model during strain hardening-softening can be in term of accumulative plastic strain. This model can calculate the stress-strain curves of clayed soils accurately.

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A Constitutive Model of Sandstone Considering the Post Peak Behavior

Journal of Mechanics ◽

10.1017/jmech.2017.71 ◽

2017 ◽

Vol 35 (1) ◽

pp. 13-25 ◽

Cited By ~ 3

Author(s):

F. S. Jeng ◽

M. C. Weng ◽

F. H. Yeh ◽

Y. H. Yang ◽

T. H. Huang

Keyword(s):

Constitutive Model ◽

Nonlinear Elasticity ◽

Strain Curve ◽

Shear Loading ◽

Triaxial Tests ◽

Flow Rule ◽

Plastic Behavior ◽

Softening Behavior ◽

Proposed Model ◽

Confining Pressures

AbstractIn rock engineering, evaluating the post-peak strength and deformation of rock is necessary. To explore the elasto-plastic behavior of sandstone in the post-peak stage, a series of strain-controlled triaxial tests were conducted under different confining pressures. According to the post-peak characteristics, a constitutive model based on nonlinear elasticity and generalized plasticity is proposed. This proposed model is characterized by the following features: (1) Nonlinear elasticity is observed under hydrostatic and shear loading; (2) the associated flow rule is followed; (3) substantial plastic deformation occurs during shear loading; and (4) post-peak softening behavior is accurately predicted. This model requires twelve material parameters, three for elasticity and nine for plasticity. The proposed model was validated by comparing the triaxial test results of Mushan sandstone at different hydrostatic pressures under dry and saturated conditions. In addition, the model is versatile; it can simulate the deformational behavior of two other sandstones. In summary, the proposed model can reasonably predict the complete stress–strain curve of sandstone.

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Thermal effect on the thermomechanical behavior of contacts in a Traveling Wave Tube

Thermal Science ◽

10.2298/tsci141216010c ◽

2016 ◽

Vol 20 (6) ◽

pp. 1983-1990

Author(s):

Mounir Chbiki ◽

Silva da ◽

Jean-Gabriel Bauzin ◽

Najib Laraqi ◽

Jean-Francois Jarno

Keyword(s):

Mechanical Properties ◽

Contact Area ◽

Delay Line ◽

Numerical Study ◽

Heat Transfer Process ◽

Traveling Wave Tube ◽

Wave Tube ◽

Proposed Model ◽

Comparison Results ◽

Good Agreement

A new elasto-plastic study of the contact between the helix and the rods of the delay line of Traveling Waves Tubes (TWT) was realized. Our study is focused on the analysis of the hot lines shrinking phenomenon. In the studied case, unlike brazed configuration, the contact areas are not perfect, resulting in a diminution of the heat transfer process. In order to maximize the contact area and to homogenize the contact pressure, a soft thermal conductive material is coated on the helix: copper was chosen for this study. In the present work, an analytical model is used to identify the properties of the copper coating at a given temperature. We focused on the mechanical properties in order to improve the assembly process with a better numerical study. Experimental method have been made to validate the proposed model. The first comparison results seem to indicate that the model represents the reality with a good agreement. It is very clearly shown that the temperature decreases the mechanical properties. (Young?s modulus, yield strength, tensile strength?). And the thickness of the coating increases the contact area. This last point is less important at room temperature (6% of increase) than at 140?C (22%).

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Mechanical Properties and Statistical Damage Constitutive Model of Rock under a Coupled Chemical-Mechanical Condition

Geofluids ◽

10.1155/2019/7349584 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

Yun Lin ◽

Feng Gao ◽

Keping Zhou ◽

Rugao Gao ◽

Hongquan Guo

Keyword(s):

Mechanical Properties ◽

Constitutive Model ◽

Weibull Distribution ◽

Damage Evolution ◽

Chemical Corrosion ◽

Mechanical Condition ◽

Confining Pressures ◽

Damage Constitutive Model ◽

Statistical Damage Constitutive Model ◽

Statistical Damage

Chemical corrosion has a significant impact on the damage evolution behavior of rock. To investigate the mechanical damage evolution process of rock under a coupled chemical-mechanical (CM) condition, an improved statistical damage constitutive model was established using the Drucker-Prager (D-P) strength criterion and two-parameter Weibull distribution. The damage variable correction coefficient and chemical damage variable which was determined by porosity were also considered in the model. Moreover, a series of conventional triaxial compressive tests were carried out to investigate the mechanical properties of sandstone specimens under the effect of chemical corrosion. The relationship between rock mechanics properties and confining pressure was also explored to determine Weibull distribution parameters, including the shape parameter m and scale parameter F0. Then, the reliability of the damage constitutive model was verified based on experimental data. The results of this study are as follows: (i) the porosity of sandstone increased and the mechanical properties degraded after chemical corrosion; (ii) the relationships among the compressive strength, the peak axial strain, and confining pressures were linear, while the relationships among the elastic modulus, the residual strength, and confining pressures were exponential functions; and (iii) the improved statistical damage constitutive model was in good agreement with the testing curves with R2>0.98. It is hoped that the study can provide an alternative method to analyze the damage constitutive behavior of rock under a coupled chemical-mechanical condition.

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Experimental Investigation on Mechanical Properties of Soft Rock under Instantaneous Triaxial Compression

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.594-597.218 ◽

2012 ◽

Vol 594-597 ◽

pp. 218-221

Author(s):

Yu Wang ◽

Feng Liu

Keyword(s):

Mechanical Properties ◽

Shear Failure ◽

Triaxial Compression ◽

Deformation Modulus ◽

Soft Rock ◽

Confining Pressure ◽

Test System ◽

Compression Tests ◽

Confining Pressures ◽

Failure Angle

Using the RMT-150C rock mechanics test system, the instantaneous triaxial compression tests for muddy siltstone were carried out under different confining pressures, and the instantaneous mechanical properties of soft rock were obtained. The results show that the strength parameters of sample have a positive linear relation with the confining pressure, and the sensitivity of peak strength on the confining pressure is higher than that of residual strength. The elastic and deformation modulus of sample linearly increase with the confining pressure going up, and the elastic modulus is more sensitive to the confining pressure. The soft rock sample shows typical ductility failure characteristic, while the damage characteristic is mainly shear failure and the shear failure angle linearly decreases with the confining pressure going up.

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Higher-Order Thinking Skills (HOTS)-based Formative Assessment: A Proposed Model for Language Learning Assessment

Vision Journal for Language and Foreign Language Learning ◽

10.21580/vjv9i25859 ◽

2020 ◽

Vol 9 (2) ◽

pp. 115

Author(s):

Wiyaka Wiyaka ◽

Entika Fani Prastikawati ◽

AB Prabowo Kusumo Adi

Keyword(s):

Formative Assessment ◽

Language Learning ◽

Higher Order Thinking ◽

Thinking Skills ◽

Higher Order ◽

Formative Assessments ◽

Assessment Model ◽

Higher Order Thinking Skills ◽

Learning Assessments ◽

Proposed Model

<div><p class="StyleABSTRAKenCambria">The integration of higher-order thinking skills (HOTS) in language learning assessments has become a crucial issue in 21st-century learning. However, not many teachers are aware of the need to incorporate HOTS in assessments due to their insufficient knowledge and the absence of good examples. Further, there is not much research and literature on HOTS-based formative assessment that can be used as references. This research aims to fill the existing gap by providing a model of higher-order thinking skills (HOTS)-based formative assessments for English learning, especially in junior high schools. By employing research and development design, this research describes the validation of the assessment model. The proposed model of assessment may be used as a prototype for assessing language learning.</p></div><p> </p>

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On the Dragging Trajectory of Anchors in Clay for Merchant Ships

Journal of Marine Science and Engineering ◽

10.3390/jmse9020118 ◽

2021 ◽

Vol 9 (2) ◽

pp. 118

Author(s):

Xinqing Zhuang ◽

Keliang Yan ◽

Pan Gao ◽

Yihua Liu

Keyword(s):

Mathematical Model ◽

Structural Integrity ◽

Indirect Measurement ◽

Test System ◽

Flow Rule ◽

Burial Depth ◽

Proposed Model ◽

Depth Increase ◽

Two Parameters ◽

The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

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A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Polymers ◽

10.3390/polym13091393 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1393

Author(s):

Xiaochang Duan ◽

Hongwei Yuan ◽

Wei Tang ◽

Jingjing He ◽

Xuefei Guan

Keyword(s):

Composite Materials ◽

Constitutive Model ◽

Model Parameters ◽

Temperature Dependent ◽

Stress Strain ◽

Proposed Model ◽

Single Temperature ◽

Testing Data ◽

Bonded Composite ◽

Tension And Compression

This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

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Towards Recognition of Scale Effects in a Solid Model of Lattices with Tensegrity-Inspired Microstructure

Solids ◽

10.3390/solids2010002 ◽

2021 ◽

Vol 2 (1) ◽

pp. 50-59

Author(s):

Wojciech Gilewski ◽

Anna Al Sabouni-Zawadzka

Keyword(s):

Mechanical Properties ◽

Continuum Model ◽

Scale Effects ◽

Theory Of Elasticity ◽

Solid Model ◽

Gradient Theory ◽

General Description ◽

Normal Forces ◽

Second Gradient ◽

Proposed Model

This paper is dedicated to the extended solid (continuum) model of tensegrity structures or lattices. Tensegrity is defined as a pin-joined truss structure with an infinitesimal mechanism stabilized by a set of self-equilibrated normal forces. The proposed model is inspired by the continuum model that matches the first gradient theory of elasticity. The extension leads to the second- or higher-order gradient formulation. General description is supplemented with examples in 2D and 3D spaces. A detailed form of material coefficients related to the first and second deformation gradients is presented. Substitute mechanical properties of the lattice are dependent on the cable-to-strut stiffness ratio and self-stress. Scale effect as well as coupling of the first and second gradient terms are identified. The extended solid model can be used for the evaluation of unusual mechanical properties of tensegrity lattices.

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