scholarly journals Dynamic triaxial constitutive model for rock subjected to initial stress

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 149-163
Author(s):  
Junzhe Li ◽  
Guang Zhang ◽  
Mingze Liu ◽  
Shaohua Hu ◽  
Xinlong Zhou
Keyword(s):  
Constitutive Model ◽  
Impact Load ◽  
Three Dimensional ◽  
Estimation Method ◽  
Constant Strain Rate ◽  
Strain Curve ◽  
Initial Pressure ◽  
Expansion Method ◽  
Three Dimensions ◽  
Model Parameters

AbstractBuilding on the existing model, an improved constitutive model for rock is proposed and extended in three dimensions. The model can avoid the defect of non-zero dynamic stress at the beginning of impact loading, and the number of parameters is in a suitable range. The three-dimensional expansion method of the component combination model is similar to that of the Hooke spring, which is easy to operate and understand. For the determination of model parameters, the shared parameter estimation method based on the Levenberg–Marquardt and the Universal Global Optimization algorithm is used, which can be well applied to models with parameters that do not change with confinement and strain rates. According to the established dynamic constitutive equation, the stress–strain curve of rock under the coupling action of the initial hydrostatic pressure load and constant strain-rate impact load can be estimated theoretically. By comparing the theoretical curve with the test data, it is shown that the dynamic constitutive model is suitable for the rock under the initial pressure and impact load.

scholarly journals Elastoplastic Model and Three-Dimensional Method for Unsaturated Soils

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jinjin Fang ◽  
Yixin Feng
Keyword(s):  
Constitutive Model ◽  
Unsaturated Soils ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Degree Of Saturation ◽  
Triaxial Tests ◽  
Model Parameters ◽  
Elastoplastic Model ◽  
True Triaxial ◽  
Elastoplastic Constitutive Model

This paper proposed a new elastoplastic constitutive model to predict the deformation and strength behaviour of unsaturated soils. Applying the modified Cambridge model as a generalization, the degree of saturation is introduced into the elastoplastic model of unsaturated soil. Under the condition of ensuring that the model parameters are unchanged, the model is transformed into three dimensions based on the SMP criterion transformation stress method. Enhanced modified van Genuchten model under true triaxial conditions is also proposed in this paper to describe hydromechanical behaviours of unsaturated soils. The proposed constitutive model can capture the observed mechanical and hydraulic behaviours. Then, the model is validated via equal p and equal b value true triaxial tests, and the results show that a reasonable agreement can be obtained.

The Studies of Rock Damage Softening Statistical Constitutive Model under True Triaxial Stress State

2014 ◽  
Vol 580-583 ◽  
pp. 312-315
Author(s):  
Hui Mei Zhang ◽  
Xiang Miao Xie ◽  
Geng She Yang
Keyword(s):  
Constitutive Model ◽  
Strain Curve ◽  
Stress Path ◽  
Complex Stress ◽  
Model Parameters ◽  
Stress Strain ◽  
Deformation And Failure ◽  
True Triaxial ◽  
Complex Stress Path ◽  
The Impact

From the feature of rock micro-unit failure obeys Poisson random distribution, the damage softening statistical constitutive of was established under true triaxial confinement based on D-P criterion, so the impact of the intermediate principal stress on rock deformation and failure was considered in theory, and the actual engineering rock complex stress path evolution was reflected more realistically. Furthermore, according to the geometrical conditions of stress-strain relationship, the theoretical relationship between constitutive model parameters and the stress-strain curve characteristic parameters during the process of rock softening and deforming, which enhance the adaptability of the model. Finally, the rationality of the model verified by the measured data.

Three-dimensional effects in low-strain integrity testing of piles: analytical solution

2016 ◽  
Vol 53 (2) ◽  
pp. 225-235 ◽  
Author(s):  
Changjie Zheng ◽  
George P. Kouretzis ◽  
Xuanming Ding ◽  
Hanlong Liu ◽  
Harry G. Poulos
Keyword(s):  
Impact Load ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Integrity Testing ◽  
Integrity Tests ◽  
The One ◽  
Propagation Of Waves ◽  
The Impact ◽  
Pile Integrity ◽  
Elastic Soil

The interpretation of low-strain integrity tests of piles is commonly based on methods developed around the one-dimensional wave propagation theory. In reality, waves resulting from the impact of a hammer on a pile head propagate in three dimensions, and the validity of the plane-front assumption is rather questionable for cases where the size of the hammer is small relative to that of the pile. This paper presents an analytical model of the dynamic response of a pile to an impact load on its head, considering propagation of waves in both vertical and radial directions. The proposed formulation applies to a pile of finite length embedded in multilayered elastic soil, and allows for considering both shape and material pile defects, by reducing locally the radius of the pile cross section or the Young’s modulus of its material. Arithmetic examples are used to depict the effect of high-frequency interferences on the interpretation of pile integrity tests, which can only be accounted for in the three-dimensional formulation of the problem, and lead to practical suggestions for the interpretation of such tests.

scholarly journals Study of Damage Constitutive Model of Brittle Rocks considering Stress Dropping Characteristics

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Fei Li ◽  
Shuang You ◽  
Hongguang Ji ◽  
Hao Wang
Keyword(s):  
Constitutive Model ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Brittle Rock ◽  
Model Parameters ◽  
Deformation And Failure ◽  
Brittle Rocks ◽  
Whole Process ◽  
Confining Pressures ◽  
Damage Constitutive Model

Deep brittle rock exhibits characteristics of rapid stress dropping rate and large stress dropping degree after peak failure. To simulate the whole process of deformation and failure of the deep brittle rock under load, the Lemaitre strain equivalent theory is modified to make the damaged part of the rock has residual stress. Based on the damage constitutive model considering residual strength characteristics, a correction factor reflecting stress dropping rate is added, the Weibull distribution is used to describe the inhomogeneity of rock materials, and Drucker–Prager criterion is used to quantitatively describe the influence of stress on damage; a damage constitutive model of deep brittle rock considering stress dropping characteristics is established. According to the geometric features of the rock stress-strain curve, the theoretical expressions of model parameters are derived. To verify the rationality of the model, triaxial compression experiments of deep brittle rock under different confining pressures are conducted. And the influence of model parameters on rock mechanical behaviour is analysed. The results show that the model reflects the stress dropping characteristics of deep brittle rock and the theoretical curve is in good agreement with the experimental results, which indicates that the proposed constitutive model is scientific and feasible.

scholarly journals Modeling Gravity-Dependent Plasticity of the Angular Vestibuloocular Reflex With a Physiologically Based Neural Network

2006 ◽  
Vol 96 (6) ◽  
pp. 3349-3361 ◽  
Author(s):  
Yongqing Xiang ◽  
Sergei B. Yakushin ◽  
Bernard Cohen ◽  
Theodore Raphan
Keyword(s):  
Neural Network ◽  
Three Dimensional ◽  
Learning Rule ◽  
Three Dimensions ◽  
Head Orientation ◽  
Model Parameters ◽  
Vestibuloocular Reflex ◽  
Model Predictions ◽  
Physiologically Based ◽  
Head Positions

A neural network model was developed to explain the gravity-dependent properties of gain adaptation of the angular vestibuloocular reflex (aVOR). Gain changes are maximal at the head orientation where the gain is adapted and decrease as the head is tilted away from that position and can be described by the sum of gravity-independent and gravity-dependent components. The adaptation process was modeled by modifying the weights and bias values of a three-dimensional physiologically based neural network of canal–otolith-convergent neurons that drive the aVOR. Model parameters were trained using experimental vertical aVOR gain values. The learning rule aimed to reduce the error between eye velocities obtained from experimental gain values and model output in the position of adaptation. Although the model was trained only at specific head positions, the model predicted the experimental data at all head positions in three dimensions. Altering the relative learning rates of the weights and bias improved the model-data fits. Model predictions in three dimensions compared favorably with those of a double-sinusoid function, which is a fit that minimized the mean square error at every head position and served as the standard by which we compared the model predictions. The model supports the hypothesis that gravity-dependent adaptation of the aVOR is realized in three dimensions by a direct otolith input to canal–otolith neurons, whose canal sensitivities are adapted by the visual-vestibular mismatch. The adaptation is tuned by how the weights from otolith input to the canal–otolith-convergent neurons are adapted for a given head orientation.

Thermoacoustic Modeling of a Graphene-Based Actuator

2014 ◽  
Author(s):  
Jonghoon Bin ◽  
William S. Oates ◽  
Kunihiko Taira
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Model Parameters ◽  
Three Dimensional Model ◽  
Mcmc Algorithms ◽  
Flux Boundary Conditions ◽  
Model Parameter Uncertainty ◽  
The One ◽  
Different Characteristics ◽  
Surface Temperature Variation

A model for two-dimensional graphene-based thermoacoutic membranes is investigated analytically and validated numerically in this study. In one-dimension, the temperature and the pressure variables are analytically determined by decoupling the two variables in the governing equations due to the large disparity between length scales. We further extend the one-dimensional findings to three dimensions. The three-dimensional pressure fluctuation produced by the surface temperature variation is determined with the aid of the acoustic piston model. Through the one and three-dimensional model analysis, the dependence of acoustic pressure as a function of frequency is studied and the acoustic response with respect to the frequency shows different characteristics when assuming Dirichlet (temperature) or Neumann (heat flux) boundary conditions. The general thermoacoustic model is then applied to a graphene-on-paper sound device. Probabilistic Bayesian method coupled with Monte Carlo Markov Chain (MCMC) algorithms is used to optimize model parameters and to analyze model parameter uncertainty. Excellent correlations of thermoacoustic behavior is predicted by the model which provides insight into heat transport mechanisms associated with generating sound from thermally cycling graphene at high frequencies.

scholarly journals Study on Damage Statistical Constitutive Model of Triaxial Compression of Acid-Etched Rock under Coupling Effect of Temperature and Confining Pressure

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7414
Author(s):  
Youliang Chen ◽  
Peng Xiao ◽  
Xi Du ◽  
Suran Wang ◽  
Zhoulin Wang ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Coupling Effect ◽  
Triaxial Compression ◽  
Strain Curve ◽  
Confining Pressure ◽  
Effect Of Temperature ◽  
Acid Etching ◽  
Model Parameters ◽  
Stress Strain Curve ◽  
Stress Strain

Based on Lemaitre’s strain equivalence hypothesis theory, it is assumed that the strength of acid-etching rock microelements under the coupling effect of temperature and confining pressure follows the Weibull distribution. Under the hypothesis that micro-element damage meets the D-P criterion and based on continuum damage mechanics and statistical theory, chemical damage variables, thermal damage variables and mechanical damage variables were introduced in the construction of damage evolution equations and constitutive models for acid-etching rocks considering the coupled effects of temperature and confining pressure. The required model parameters were obtained by theoretical derivation, and the model was verified based on the triaxial compression test data of granite. Comparing the experimental stress-strain curve with the theoretical stress-strain curve, the results show that they were in good agreement. By selecting reasonable model parameters, the damage statistical constitutive model can accurately reflect the stress-strain curve characteristics of rock in the process of triaxial compression. The comparison between the experimental and theoretical results also verifies the reasonableness and reliability of the model. This model provides a new rock damage statistical constitutive equation for the study of rock mechanics and its application in engineering, and has certain reference significance for rock underground engineering.

Calibration and Validation of Multiscale Model for Ultimate Strength Prediction of Composite Laminates Under Uncertainty

2021 ◽  
Author(s):  
Rudraprasad Bhattacharyya ◽  
Sankaran Mahadevan
Keyword(s):  
Constitutive Model ◽  
Composite Laminates ◽  
Damage Mechanics ◽  
Epistemic Uncertainty ◽  
Three Dimensional ◽  
Continuum Damage Mechanics ◽  
Multiscale Model ◽  
Strength Prediction ◽  
Model Parameters ◽  
Modeling Framework

Abstract A methodology to account for the effect of epistemic uncertainty (regarding model parameters) on the strength prediction of carbon fiber reinforced polymer (CFRP) composite laminates is presented. A three-dimensional concurrent multiscale physics modeling framework is considered. A continuum damage mechanics-based constitutive relation is used for multiscale analysis. The parameters for the constitutive model are unknown and need to be calibrated. A least squares-based approach is employed for the calibration of model parameters and a model discrepancy term. The calibrated constitutive model is validated quantitatively using experimental data for both unnotched and open-hole specimens with different composite layups. The quantitative validation results are used to indicate further steps for model improvement.

THREE-DIMENSIONAL PERISTALTIC FLOW OF A WILLIAMSON FLUID IN A RECTANGULAR CHANNEL HAVING COMPLIANT WALLS

2014 ◽  
Vol 14 (01) ◽  
pp. 1450002 ◽  
Author(s):  
R. ELLAHI ◽  
ARSHAD RIAZ ◽  
S. NADEEM
Keyword(s):  
Fluid Model ◽  
Rectangular Channel ◽  
Three Dimensional ◽  
Expansion Method ◽  
Peristaltic Flow ◽  
Three Dimensions ◽  
Physical Parameters ◽  
Williamson Fluid ◽  
Eigenfunction Expansion Method ◽  
Compliant Walls

In this study, the mathematical observations for the peristaltic flow of a Williamson fluid model (e.g., chyme) in a cross-section of a rectangular duct having compliant walls were considered. The flow was assumed incompressible and unsteady. The constitutive equations were reduced under the assumptions of low Reynolds number and long wavelength approximations. The resulting dimensionless governing equations were solved using the homotopy perturbation method (HPM) and eigenfunction expansion method. The results obtained were explained graphically. The velocity distribution was plotted for physical parameters both in two and three dimensions. The streamline graphs are presented in the end, which explain the trapping bolus phenomenon. All theoretical and graphical results are then discussed simultaneously.

On the Extraction of Elastic–Plastic Constitutive Properties From Three-Dimensional Deformation Measurements

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
A. J. Gross ◽  
K. Ravi-Chandar
Keyword(s):  
Constitutive Model ◽  
Tensile Test ◽  
Three Dimensional ◽  
Image Correlation ◽  
Uniaxial Tensile ◽  
Model Parameters ◽  
Material Models ◽  
Elastic Plastic ◽  
Constitutive Properties ◽  
Deformation Measurements

In this article, a coupled experimental and numerical method is utilized for characterizing the elastic–plastic constitutive properties of ductile materials. Three-dimensional digital image correlation (DIC) is used to measure the full field deformation on two mutually orthogonal surfaces of a uniaxial tensile test specimen. The material’s constitutive model, whose parameters are unknown a priori, is determined through an optimization process that compares these experimental measurements with finite element simulations in which the constitutive model is implemented. The optimization procedure utilizes the robust dataset of locally observed deformation measurements from DIC in addition to the standard measurements of boundary load and displacement data. When the difference between the experiment and simulations is reduced sufficiently, a set of parameters is found for the material model that is suitable to large strain levels. This method of material characterization is applied to a tensile specimen fabricated from a sheet of 15-5 PH stainless steel. This method proves to be a powerful tool for calibration of material models. The final parameters produce a simulation that tracks the local experimental displacement field to within a couple percent of error. Simultaneously, the percent error in the simulation for the load carried by the specimen throughout the test is less than 1%. Additionally, half of the parameters for Hill’s yield criterion, describing anisotropy of the normal stresses, are found from a single tensile test. This method will find even greater utility in calibrating more complex material models by greatly reducing the experimental effort required to identify the appropriate model parameters.

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