A Reformation of the Equations of Anisotropic Poroelasticity

1991 ◽  
Vol 58 (3) ◽  
pp. 612-616 ◽  
Author(s):  
M. Thompson ◽  
J. R. Willis
Keyword(s):  
Pore Pressure ◽  
Constitutive Equations ◽  
Isotropic Material ◽  
Transverse Isotropy ◽  
Material Behavior ◽  
Solid Skeleton ◽  
Porous Rocks ◽  
Testing Procedures ◽  
Fluid Content ◽  
Mean Strain

The constitutive equations of linear poroelasticity presented by Biot (1955) and Biot and Willis (1957) extended the description of rock behavior into the realm of saturated porous rocks. For isotropic material behavior, Rice and Cleary (1976) gave a formulation which involved material constants whose physical interpretation was particularly simple and direct; this is an aid both to their measurement and to the interpretation of predictions from the theory. This paper treats anisotropic poroelasticity in terms of material tensors with interpretations similar to those of the constants employed by Rice and Cleary. An effective stress principle is derived for such anisotropic material. The material tensors are defined, rigorously, from the stress field and pore fluid content changes produced by boundary displacements compatible with a uniform mean strain and uniform pore pressure increments. Such displacements and pore pressure increments lead to homogeneous deformation on all scales significantly larger than the length scale of microstructural inhomogeneities. This macroscopic behavior is related to the microscopic behavior of the solid skeleton. The tensors which describe the microscopic behavior of the solid skeleton would be difficult, even impossible, to measure, but their introduction allows relationships between measurable quantities to be identified. The end product of the analysis is a set of constitutive equations in which the parameters are all measurable directly from well-accepted testing procedures. Relationships exist between measurable quantities that can be used to verify that the constitutive equations described here are valid for the rock under consideration. The case of transverse isotropy is discussed explicitly for illustration.

scholarly journals A Nonlinear Statistical Damage Constitutive Model for Porous Rocks

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yue Pan ◽  
Zhiming Zhao ◽  
Liu He ◽  
Guang Wu
Keyword(s):  
Constitutive Model ◽  
Solid Skeleton ◽  
Porous Rocks ◽  
Different Types ◽  
Confining Pressures ◽  
Damage Constitutive Model ◽  
Statistical Damage Constitutive Model ◽  
Energy Theory ◽  
Water Contents ◽  
Statistical Damage

In the current paper, the deformation behaviours of rocks during compression are studied by testing 10 groups of sandstone samples with different porosity characteristics. According to the energy theory, the rock material was divided into two parts: solid skeleton and voids. A statistical damage-based approach was adopted to establish a nonlinear statistical damage constitutive model. The validity of the statistical damage constitutive model is verified by the test data. The statistical damage constitutive model performs well in each stage of rock compression before failure. For different types of rocks, different confining pressures, and different water contents, the statistical damage constitutive model fits well. This model can be applied to most types of rocks and in most engineering environments.

Toward phenomenological universality of the mechanical behavior of arbitrarily anisotropic porous rocks

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA167-WA183 ◽  
Author(s):  
Patrick N. J. Rasolofosaon
Keyword(s):  
Mechanical Behavior ◽  
Empirical Relation ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Porous Network ◽  
Hooke’S Law ◽  
Fluid Content ◽  
Elastic Hysteresis ◽  
Hydraulic Hysteresis ◽  
Hooke's Law

The great diversity of the microstructures of rocks impedes the use of a universal rock physics model with idealized geometry to correctly describe the mechanical behavior of rocks. In this quest for universality, by ignoring the detailed description of the causes of the observed phenomenon and only focusing on the empirical relation between the cause (applied stress) and the effect (resulting strain), phenomenological models such as the linear elastic Hooke’s law roughly describe the mechanical behavior of rocks of contrasted microstructures. However, in detail, numerous laboratory experiments covering broad frequency and strain ranges (both typically more than eight orders of magnitude) on various types of rocks have also shown deviations from Hooke’s law due to anisotropy, frequency dependence, nonlinearity, possibly with the presence of hysteresis, and poroelasticity. A phenomenological model has been recently proposed that synthesizes all these behaviors in a single model, but unfortunately does not integrate the porous nature of rocks. The new model is based on a reformulation in modified spectral decomposition of the previous work using the 7D poroelastic tensor linking the dynamic parameters (i.e., the six stress components and fluid pressure) and the kinematic parameters (i.e., the six strain components and the local increase of fluid content ζ). In addition to the elastic hysteresis of the stress-strain curves, the model also predicts the existence of a second hysteresis, or hydraulic hysteresis, of the curve fluid pressure p versus fluid content ζ, qualitatively similar to the first one. Indeed, the elastic hysteresis is due to the opening and the closure of some compliant pores at different stress levels. These pores represent possible access radii for the saturating fluid; the hysteresis in the geometry of the porous network also induces the hydraulic hysteresis in the p-ζ curves.

Modeling and Analysis of Elastoplastic Impacts on Supported Composites

2011 ◽  
Vol 471-472 ◽  
pp. 367-372 ◽  
Author(s):  
Majed A. Majeed ◽  
Ahmet S. Yigit ◽  
Andreas P. Christoforou
Keyword(s):  
Isotropic Material ◽  
Composite Layer ◽  
Transversely Isotropic ◽  
Material Behavior ◽  
Model Parameters ◽  
Fe Model ◽  
Transversely Isotropic Material ◽  
Spherical Object ◽  
Modeling And Analysis ◽  
Plastic Indentation

This paper presents an elastoplastic impact model for a spherical object impacting a supported composite layer or a half-space. The model utilizes a contact law that has been developed based on elastic-plastic and fully plastic indentation theories. For an impact event, the model parameters can easily be obtained analytically, computationally using Finite Elements (FE), and from experiments, by assuming transversely isotropic material behavior. Simulations are compared to those from a nonlinear FE model developed in ABAQUS, and to limited experimental data, with excellent results.

Anisotropy: Benefits for UOE Line Pipe

2012 ◽  
Author(s):  
Oliver Hilgert ◽  
Steffen Zimmermann ◽  
Christoph Kalwa
Keyword(s):  
Anisotropic Material ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Structural Response ◽  
Bending Moment ◽  
Yield Function ◽  
Material Behavior ◽  
Load Case ◽  
Line Pipe ◽  
Anisotropic Plastic

Plastic anisotropic material behavior of UOE line pipe is investigated in view of its structural response. Common load cases are considered and their resultant strain capacity concerning Strain Based Design demands are discussed. Hill’s yield function is used to analyze steel line pipe under internal pressure and bending moment. Here, a three-dimensional anisotropic plastic strain evolution is considered. It was shown, that underlying anisotropic material behavior can be beneficial for the structural response of line pipe, although it depends on the load case and the directional anisotropy. That is in some way contrary to the demands in specifications, where isotropic material behavior is desired.

Material Behavior Under Thermal Loading

1986 ◽  
Vol 108 (1) ◽  
pp. 113-119 ◽  
Author(s):  
Huseyin Sehitoglu
Keyword(s):  
Mechanical Loading ◽  
Constitutive Equations ◽  
Thermal Loading ◽  
Mechanical Deformation ◽  
Cyclic Stress ◽  
Material Behavior ◽  
Temperature History ◽  
Strain History ◽  
History Effects ◽  
Temperature Strain

Material behavior under thermo-mechanical and isothermal loading cases is studied. The influence of constraint on thermo-mechanical deformation behavior is identified using a two-bar structure. Some of the possible microstructural mechanisms that may be operative under thermo-mechanical loading conditions are discussed. Isothermal tests are reported in the temperature range 20 to 600°C. Additional isothermal tests with step increases and decreases in temperature are performed to study the influence of temperature history on material behavior. During these tests, transient material behavior indicated temperature-strain history effects. Constitutive equations that capture essential features of material behavior under isothermal and thermo-mechanical loading cases are examined. Preliminary predictions of cyclic stress-strain loops are compared to experimental response. Further work is needed to incorporate temperature-strain history effects into constitutive equations.

Dynamic Characterization of Vertically Aligned Carbon Nanotube Pads for Materials Handling Applications

2016 ◽  
Author(s):  
Nicholas Candelino ◽  
Nader Jalili
Keyword(s):  
Experimental Data ◽  
Carbon Nanotube ◽  
Impact Testing ◽  
Low Energy ◽  
Material Behavior ◽  
Practical Implementation ◽  
Testing Procedures ◽  
Vector Correlation ◽  
Energy Impact ◽  
Vertically Aligned

Vertically-aligned carbon nanotube (VACNT) pads have recently received widespread attention for use as contact surfaces in material handling processes that involve the transfer of bare silicon wafers. Such processes will benefit from the strong friction force interactions and minimal adhesion force offered by these pads, allowing the wafer to be picked up, carried, and quickly placed, without encountering problems which may arise due to excessive adhesive forces. Despite these benefits, practical implementation has been hindered because VACNTs have nonlinear mechanical characteristics which are still not well understood. Consequently, significant attention has been devoted to fully understand and determine the behaviors associated with their nonlinear dynamic mechanical properties. Along this line, several experimental techniques are applied in this paper to further develop a comprehensive understanding of the mechanical behavior of these pads under compressive loading. It is important to note that the samples used in this testing are not standard VACNTs, but have been grown separately from the final substrate on which they are mounted during testing. After growth, the samples are turned upside-down and fixed so that the bottom ends of all VACNTs are planar and present an ultra-flat top surface for contact during manipulation. The tests performed in this research include a low energy impact test and position controlled load-displacement testing with both constant and sinusoidal velocity loading and unloading. Through these testing procedures, the dependencies of the VACNT material properties to compression depth and displacement rate are observed and an attempt is made to incorporate them into a continuous model. For this, the results from the low energy impact testing provide grounds to state the nature of the nonlinear behavior in our VACNTs. By interrogating the available data from each testing technique, a combination of information provided by the theoretical energy balance and the identified coefficients from the Levenberg-Marquardt curve-fitting algorithm is then applied to generate a parametrized phenomenological model of the VACNT pad behavior. The proposed identified model is continuous and reasonably accounts for the overall material behavior as seen in the experimental data. The validity of this model is shown by means of normalized vector correlation of over 99% between the results of the numerical simulations and the existing experimental data. The material behaviors observed in this research qualitatively support those of several earlier investigators who have previously recognized the complex dissipative behavior of VACNTs. The proposed work itself paves the road for developing a useful engineering model of VACNT pad dynamics which will enable their introduction to mechanical applications in industry.

The effect of pore pressure depletion and injection cycles on ultrasonic velocity and quality factor in a quartz sandstone

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. E43-E51 ◽  
Author(s):  
P. Frempong ◽  
A. Donald ◽  
S. D. Butt
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Axial Strain ◽  
Fluid Pressure ◽  
Porous Rocks ◽  
Confining Stress ◽  
Viscoelastic Deformation ◽  
Experimental Conditions ◽  
Pore Pressures ◽  
Pressure Depletion

Passing seismic waves generate transient pore-pressure changes that influence the velocity and attenuation characteristics of porous rocks. Compressional ultrasonic wave velocities [Formula: see text] and quality factors [Formula: see text] in a quartz sandstone were measured under cycled pore pressure and uniaxial strain conditions during a laboratory simulated injection and depletion process. The objectives were to study the influence of cyclical loading on the acoustic characteristics of a reservoir sandstone and to evaluate the potential to estimate pore-fluid pressure from acoustic measurements. The values of [Formula: see text] and [Formula: see text] were confirmed to increase with effective stress increase, but it was also observed that [Formula: see text] and [Formula: see text] increased with increasing pore pressure at constant effective stress. The effective stress coefficient [Formula: see text] was found to be less thanone and dependent on the pore pressure, confining stress, and load. At low pore pressures, [Formula: see text] approached one and reduced nonlinearly at high pore pressures. The change in [Formula: see text] and [Formula: see text] with respect to pore pressure was more pronounced at low versus high pore pressures. However, the [Formula: see text] variation with pore pressure followed a three-parameter exponential rise to a maximum limit whereas [Formula: see text] had no clear limit and followed a two-parameter exponential growth. Axial strain measurements during the pore-pressure depletion and injection cycles indicated progressive viscoelastic deformation in the rock. This resulted in an increased influence on [Formula: see text] and [Formula: see text] with increasing pore-pressure cycling. The value [Formula: see text] was more sensitive in responding to the loading cycle and changes in pore pressures than [Formula: see text]; thus, [Formula: see text] may be a better indicator for time-lapse reservoir monitoring than [Formula: see text]. However, under the experimental conditions, [Formula: see text] was unstable and difficult to measure at low effective stress.

Cycle-Dependent Stress Relaxation of A-286 Alloy

1960 ◽  
Vol 82 (3) ◽  
pp. 654-658 ◽  
Author(s):  
A. S. Ross ◽  
JoDean Morrow
Keyword(s):  
Fatigue Life ◽  
Material Behavior ◽  
Mean Stress ◽  
Fatigue Specimen ◽  
Fatigue Data ◽  
The Mean ◽  
Cycle Dependent ◽  
Mean Strain ◽  
Mean Stresses ◽  
Strain Cycling

When an axial fatigue specimen is subjected to repeated strain cycling about a fixed mean strain value, the mean stress decreases with the number of strain cycles. To explore this type of material behavior, tubular fatigue specimens of A-286 alloy have been axially tested under conditions of controlled strain, and the cycle-dependent relaxation of mean stress measured. Fatigue data for five initial mean stresses are also reported. It was found that, in the case of A-286 alloy, most of the relaxation occurred early in the fatigue life, especially during the first ten cycles.

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