Non-Coaxial Plasticity Constitutive Modeling of Sands

2013 ◽  
Vol 684 ◽  
pp. 150-153 ◽  
Author(s):  
Ping Hu ◽  
Mao Song Huang ◽  
Deng Gao Wu
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Principal Stress ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Strain Increment ◽  
Stress Axis ◽  
Shear Tests ◽  
Plastic Strain Increment ◽  
Principal Axes

Classical coaxial plasticity constitutive models implicate an inevitable limitation that directions for principal stress and that for principal plastic strain increment are always coaxial. They are not capable of simulating non-coaxial phenomena during the rotation of principal stress axis. In this paper, a three-dimensional, non-coaxial plasticity constitutive model for sands with a modification of Lade angle dependent shape function is introduced to describe the non-coaxial behavior under principal axes rotation. A series of numerical simulations of hollow cylindrical torsional shear tests are performed. The results show that the proposed constitutive model can predict the variations of principal plastic strain increment directions with principal stress directions reasonably.

scholarly journals On Computational Modelling Of Strain-Hardening Material Dynamics

2012 ◽  
Vol 11 (5) ◽  
pp. 1525-1546 ◽  
Author(s):  
Philip Barton ◽  
Evgeniy Romenski
Keyword(s):  
Relaxation Time ◽  
Stress Relaxation ◽  
Plastic Strain ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Computational Modelling ◽  
Constitutive Models ◽  
Successful Implementation ◽  
Hardening Material ◽  
Dislocation Mechanics

AbstractIn this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suitable irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided. The success of the proposed approach centres on determination of a rate-independent relation between plastic strain and entropy, which is found to be suitably simplistic such to not add any significant complexity to the final model. The result is sufficiently general to be used in combination with existing constitutive models for inelastic deformations parametrised by one-dimensional plastic strain provided the constitutive models are thermodynamically consistent. Here a model for the tangential stress relaxation time based upon established dislocation mechanics theory is calibrated for OFHC copper and subsequently integrated within a two-dimensional moving-mesh scheme. We address some of the numerical challenges that are faced in order to ensure successful implementation of the proposedmodel within a hydrocode. The approach is demonstrated through simulations of flyer-plate and cylinder impacts.

scholarly journals Analysis of Three-Dimensional Damage Constitutive Model of Frozen Sand Based on the Influence of Intermediate Principal Stress and Temperature

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Shilong Ma ◽  
Zhaoming Yao ◽  
Shuang Liu ◽  
Xuan Pan
Keyword(s):  
Constitutive Model ◽  
Weibull Distribution ◽  
Principal Stress ◽  
Three Dimensional ◽  
Intermediate Principal Stress ◽  
Frozen Soil ◽  
Stress Coefficient ◽  
Frozen Sand ◽  
Distribution Parameters ◽  
Damage Constitutive Model

To study the mechanical properties of frozen soil, it is necessary to understand the damage characteristics of frozen soil. Four types of three-dimensional indoor tests of frozen sand were carried out at −5°C, −10°C, and −15°C to study the mechanical damage properties. These include different stress path tests with the principal stress coefficients of 0, 0.25, 0.5, and 0.75 while analyzing the entire failure process. First, the three-dimensional compression test of frozen sand was studied to analyze the influence of temperature and intermediate principal stress coefficient on the large principal stress of frozen soil. The damage cost of frozen sand under the influence of different temperatures and intermediate principal stress coefficients was also established. Second, using the characteristics of discreteness and randomness of the distribution of the microelements inside the frozen soil and assuming that the failure of the microelement of the frozen soil obeys the Weibull distribution, the Drucker–Prager strength criterion was used as the statistical distribution variable of the microelement of the frozen soil based on the strain equivalence hypothesis, statistical theory, and continuous damage mechanics. This allows for a constitutive model of frozen sand damage under the three-dimensional stress state to be established. Finally, the model parameter values through low-temperature three-dimensional test data were able to be determined. This model allows for the physical meaning of Weibull distribution parameters F0 and m to be analyzed, and the distribution parameters with temperature and intermediate principal stress coefficient can be modified to obtain a modified frozen sand damage constitutive model. The results show that the modified damage constitutive model can simulate the entire process curve of the large principal stress-strain of frozen sand. It shows that the large principal stress of frozen sand increases with the increase of temperature and intermediate principal stress coefficient. Concurrently, the frozen sand damage constitutive model proposed in this paper can describe the deformation behavior of frozen soil under different temperature and stress paths and can be adapted to various other sediment types.

A Modified Microplane Model Using Transformation Surfaces to Consider Loading History on Phase Transition in Shape Memory Alloys

2014 ◽  
Author(s):  
Milad Shirani ◽  
Reza Mehrabi ◽  
Masood Taheri Andani ◽  
Mahmoud Kadkhodaei ◽  
Mohammad Elahinia ◽  
...  
Keyword(s):  
Free Energy ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Phenomenological Approach ◽  
Material Point ◽  
Loading History ◽  
Energy Potential ◽  
Microplane Model ◽  
Thermodynamic Driving Force

In most of the existing SMA constitutive models, it is assumed that transformation starts when a thermodynamic driving force reaches a specified amount regardless of loading history. In this work, a phenomenological approach is used to develop an enhanced one-dimensional constitutive model in which loading history is directly considered as one of the main parameters affecting the transformation start conditions. To generalize the model to three-dimensional cases, a microplane formulation based on volumetric-deviatoric is employed. A free energy potential is defined at the microplane level, integrated over all orientations at a material point to provide the macroscopic free energy. Experiments are carried out on Nitinol superelastic tubes to validate the newly proposed constitutive model. In these experiments, interruptions are applied during transformations to show the effects of loading history on transformation start conditions. Numerical results are compared with the experimental data to demonstrate the accuracy of the enhanced model.

scholarly journals A Rheological Model of Sandstones considering Response to Thermal Treatment

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Xingang Wang ◽  
Lei Huang ◽  
Junrong Zhang
Keyword(s):  
Thermal Treatment ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Energy Utilization ◽  
Elastic Response ◽  
Structure Damage ◽  
Rheological Response ◽  
Different Temperatures ◽  
Thermally Treated

Time-dependent rheological response of geomaterials to thermal treatment is a crucial issue in geothermal energy utilization and deep mineral mining. This response, however, has not yet been fully considered in the existing rheological constitutive models for sandstones. In order to experimentally investigate such responses and establish the associated rheological constitutive model, this study considers the sandstone specimens which have been thermally treated under different temperatures. The triaxial rheological test in conjunction with the scanning electron microscope is employed in the investigation to observe the mechanically and macro-/micromorphologically rheological response. Investigation results show that the thermal treatment induces microcracks and microdefects, and subsequently, they propagate during the creep. As a consequence, the heterogeneous deformation occurs, and macrocracks are present, leading to the irregular fluctuation and mutation in strain over time. A higher temperature contributes to a more severe structure damage and in turn reduces the intactness of sandstones and elevates the rheological response. The investigation allows successful establishment of a three-dimensional constitutive equation considering the instantaneous elastic response to thermal treatment. Based on the equation, a nonlinear visco-elastoplastic rheological constitutive model is developed for sandstones. Comparison with three existing rheological models shows that the model developed in this study could well represent the rheological process of the thermally treated sandstones.

A Theory in Finite Differences for Computation of Interchanging Principal Stresses and Principal Axes Rotation

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
S. H. Stefanov
Keyword(s):  
Principal Stress ◽  
Finite Differences ◽  
Three Dimensional ◽  
Plane Stress State ◽  
Correct Solution ◽  
Coordinate Space ◽  
Principal Stresses ◽  
Time Step ◽  
Plane State ◽  
Principal Axes

Suppose consecutive ordinates of three arbitrary and nonproportional stress-time functions of plane state of stress are entered into a computer by a little finite time step. The theory proposed solves the following problem: correct computation of the ordinates of the principal stress-time functions and the angle of principal axes rotation. This problem is not as simple as researchers approached it prior to the computer era. First of all, the correct solution for the principal stresses and the principal axes rotation require correct interchange of the principal stresses while computing them, i.e., correct interchange of the plus/minus signs in the well-known equations for them. For the interchange analysis, an ellipse of stress transformation in the three-dimensional stress-coordinate space is revealed. By changing a coordinate scale, the ellipse turns into a circumference that is an analog to, but different from, a Mohr circle. The correct solution also requires treating the principal axes rotation in little finite differences per little time differences during which little finite elements appear as building the stressing path in the three-dimensional stress-coordinate space. Based on the ellipse/circumference mentioned, three interchange conditions are revealed. The third one is the most important. And, a necessity is also revealed for dividing some stressing path's elements into two subelements. Based on all the findings, the main commands of an algorithm for computing the ordinates of the principal stress-time functions and the angle of principal axes rotation are presented. The correct solution of the problem has been achieved thanks to new notions taken from the so-called integration of damage differentials (IDD) theory. In fact, the paper presents a new contribution to the variable plane stress state analysis.

scholarly journals Large-Scale Triaxial Tests on Dilatancy Characteristics of Lean Cemented Sand and Gravel

2021 ◽  
Vol 9 ◽  
Author(s):  
Hang Yu ◽  
Xue-mei Shen ◽  
Yu-chen Ye ◽  
Jie Yang ◽  
Chen-hui Zhu
Keyword(s):  
Plastic Strain ◽  
Strain Increment ◽  
Triaxial Tests ◽  
Volume Strain ◽  
Triaxial Loading ◽  
Cemented Sand ◽  
Plastic Strain Increment ◽  
Loading And Unloading ◽  
Sand And Gravel ◽  
Increment Ratio

The dilatancy equation, which describes the plastic strain increment ratio and its dependence on the stress state, is an important component of the elastoplastic constitutive model of geotechnical materials. In order to reveal their differences of the dilatancy value determined by the total volume strain increment ratio and the real value of lean cemented sand and gravel (LCSG) materials, in this study, a series of triaxial compression tests, equiaxial loading and unloading tests, and triaxial loading and unloading tests are conducted under different cement contents and confining pressures. The results reveal that hysteretic loops appear in the stress–strain curves of equiaxial loading and unloading tests, and triaxial loading and unloading tests and that the elastic strain is an important component of the total strain. The hysteretic loop size increases with an increase in the stress level or consolidation stress, whereas the shape remains unchanged. Furthermore, with an increase in the cement content, the dilatancy value determined by the total volume strain increment ratio becomes smaller than that determined by the plastic strain increment ratio, and the influence of the elastic deformation cannot be ignored. Thus, in practical engineering scenarios, especially in the calculation of LCSG dam structures, the dilatancy equation of LCSG materials should be expressed by the plastic strain increment ratio, rather than the total volume strain increment rati.

Comparative Study on the Nonlinear Calculation of Ratcheting Deformation Using Different Constitutive Model

2020 ◽  
Author(s):  
Xuejiao Shao ◽  
Hai Xie ◽  
Furui Xiong ◽  
Xiaolong Fu ◽  
Kaikai Shi ◽  
...  
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Kinematic Hardening ◽  
Constitutive Models ◽  
Fatigue Analysis ◽  
Constitutive Law ◽  
Elastic Plastic ◽  
Bending Strain ◽  
Cumulative Strain ◽  
Membrane Strain

Abstract In the fatigue assessment of nuclear components following the RCC-M B3200, if the results using the simplified elastic-plastic method cannot meet the Code’s requirements, it is necessary to conduct a detailed elastic-plastic fatigue analysis of the component. In this paper, the A-F and Chaboche nonlinear kinematic hardening constitutive models are used to conduct an elasto-plastic fatigue analysis for a typical nozzle component, aiming to calculate the secondary cumulative cyclic plastic strain of the structure induced by the rapid temperature change transient. The calculation method of nonlinear ratcheting behavior under cyclic loading is studied. The method of determining the parameters of constitutive model based on cyclic stable stress-strain curve is also studied. A sensitive study of the parameters for the same constitutive law is presented, including the results of cumulative plastic strain. The ratcheting behavior simulation calculated by different constitutive models are compared. The results show that the A-F model has a conservative prediction of ratcheting behavior as the dynamic recovery term is too strong. It was found that the Chaboche constitutive model is the better methodology for ratcheting analysis. In order to evaluate the bearing ability of the section, the membrane strain and bending strain is obtained by linearizing the node strain along the cross section. The ratios of membrane strain and membrane plus bending strain to total strain are calculated, which is helpful to determining the limit criteria for the cumulative strain of structures.

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