Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. F13-F20 ◽  
Author(s):  
Xavier García ◽  
Ernesto A. Medina
Keyword(s):  
Cyclic Loading ◽  
Bulk Modulus ◽  
Power Law ◽  
Elastic Moduli ◽  
Effective Medium Theory ◽  
Hysteretic Behavior ◽  
Dynamics Simulation ◽  
Spherical Particles ◽  
Elastic Response ◽  
Power Law Exponent

When Hertz-Mindlin force laws are considered in the context of the effective-medium theory, the predictions yield a constant Poisson coefficient and bulk/shear elastic moduli that scale with pressure with a 1/3 power law exponent [Formula: see text]. This prediction contradicts early and recent experimental findings that conclude moduli grow faster with a 1/2 power law exponent ([Formula: see text]). Such a conclusion is also reached by recent second-order corrections to linear elastic theory. In this work we use a discrete-particle method to study the elastic response of a model of sand that is unconsolidated because of cyclic loading. We use a detailed molecular dynamics simulation that accounts for Hertz-type grain interactions and history-dependent shear forces. The porous sand model is constructed from spherical particles whose size distribution mimics well-sorted unconsolidated sands. The geometry of the model is obtained by simulating critical processes in sedimentary rock formations. Hysteretic behavior and relations between the sample bulk modulus, strain, and stress are obtained. The simulated sample reproduces experimental transient and stationary loading-unloading behavior. We find good correspondence of pressure and strain dependence of elastic moduli in our model with semilinear elasticity theory predictions. Simple arguments explain low coordination numbers observed on force-transmitting samples and the tendency to reduce dissipation under cyclic loading. Our approach clearly shows that a Hertz-Mindlin grain interaction is not inconsistent with the experimental [Formula: see text] behavior of the bulk modulus.

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

2010 ◽  
Vol 74 (2) ◽  
pp. 341-350 ◽  
Author(s):  
E. K. H. Salje ◽  
J. Koppensteiner ◽  
W. Schranz ◽  
E. Fritsch
Keyword(s):  
Bulk Modulus ◽  
Porous Materials ◽  
Power Law ◽  
Master Curve ◽  
Elastic Moduli ◽  
External Stress ◽  
Effective Elastic Moduli ◽  
Critical Porosity ◽  
Elastic Instabilities ◽  
Linear Decay

AbstractThe collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity ϕc at which small stresses will lead to the collapse of the sample. For several samples we find ϕc ~0.5 with an almost linear decay of the bulk moduli with porosity at ϕc <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law κ ~ (1–ϕm, m>2, between ϕ = 0.5 and ϕ = 1.

scholarly journals Propagation of short stress pulses in discrete strongly nonlinear tunable metamaterials

2014 ◽  
Vol 372 (2023) ◽  
pp. 20130186 ◽  
Author(s):  
Yichao Xu ◽  
Vitali F. Nesterenko
Keyword(s):  
Power Law ◽  
Elastic Moduli ◽  
Dynamic Behaviour ◽  
Spherical Particles ◽  
Short Pulses ◽  
One Dimensional ◽  
Linear Elastic ◽  
Strongly Nonlinear ◽  
Granular Chains ◽  
Different Levels

The propagation of short pulses with wavelength comparable to the size of a unit cell has been studied in a one-dimensional discrete metamaterial composed of steel discs alternating with toroidal nitrile O-rings under different levels of precompression using experiments, numerical simulations and theoretical analysis. This strongly nonlinear metamaterial is more tunable than granular chains composed of linear elastic spherical particles and has better potential for attenuation of dynamic loads. A double power-law relationship for compressed O-rings was found to describe adequately their quasi-static and dynamic behaviour with significantly different elastic moduli. It is demonstrated that the double power-law metamaterial investigated allows a dramatic increase in sound speed and acoustic impedance of three to four times using a moderate force.

Effect of the Transition Zone on the Bulk Modulus of Concrete

1994 ◽  
Vol 370 ◽  
Author(s):  
Melanie P. Lutz ◽  
Paulo J. M. Monteiro
Keyword(s):  
Bulk Modulus ◽  
Transition Zone ◽  
Cement Paste ◽  
Power Law ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Closed Form Expression ◽  
Form Expression ◽  
Effective Bulk Modulus ◽  
Model Predictions

AbstractIn concrete, non-uniformities in the hydration process, due to the the “wall effect” produeed by the aggregate (inclusion) particles, lead to an interfacial transition zone (ITZ) that is characterized by an increase in porosity near the inclusions. This increase in porosity may in turn be expected to cause a local decrease in the elastic moduli. We have modeled the effect of the ITZ by assuming that the elastic moduli vary smoothly in the vicinity of the inclusions, according to a power law. The exponent in the power law is chosen based on the estimated thickness of the ITZ. For this model, a closed-form expression can be found for the overall effective bulk modulus. The predicted bulk modulus of the concrete depends on known properties such as the elastic moduli of the bulk cement paste and the inclusions, the volume fraction of the inclusions, as well as on the elastic moduli at the interface. By comparing the model predictions to measured data, we can obtain estimates of the elastic moduli at the interface. Application of this inverse procedure to a set of data from the literature on mortar containing sand inclusions leads to the conclusion that the modulus at the interface is about 15-50% lower than in bulk cement paste.

scholarly journals A Finite Element Study on Compressive Resistance Degradation of Square and Circular Steel Braces under Axial Cyclic Loading

2021 ◽  
Vol 11 (13) ◽  
pp. 6094
Author(s):  
Hubdar Hussain ◽  
Xiangyu Gao ◽  
Anqi Shi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cyclic Loading ◽  
Slenderness Ratio ◽  
Hysteretic Behavior ◽  
Element Analysis ◽  
Section Shape ◽  
Axial Cyclic Loading ◽  
Global Buckling ◽  
Parametric Studies

In this study, detailed finite element analysis was conducted to examine the seismic performance of square and circular hollow steel braces under axial cyclic loading. Finite element models of braces were constructed using ABAQUS finite element analysis (FEA) software and validated with experimental results from previous papers to expand the specimen’s matrix. The influences of cross-section shape, slenderness ratio, and width/diameter-to-thickness ratio on hysteretic behavior and compressive-tensile strength degradation were studied. Simulation results of parametric studies show that both square and circular hollow braces have a better cyclic performance with smaller slenderness and width/diameter-to-thickness ratios, and their compressive-tensile resistances ratio significantly decreases from cycle to cycle after the occurrence of the global buckling of braces.

Regional variation of recession flow power-law exponent

2018 ◽  
Vol 32 (7) ◽  
pp. 866-872 ◽  
Author(s):  
Swagat Patnaik ◽  
Basudev Biswal ◽  
Dasika Nagesh Kumar ◽  
Bellie Sivakumar
Keyword(s):  
Power Law ◽  
Regional Variation ◽  
Power Law Exponent ◽  
Flow Power

scholarly journals Growth Rate Exponents of Richtmyer-Meshkov Mixing Layers

2005 ◽  
Vol 73 (3) ◽  
pp. 461-468 ◽  
Author(s):  
Timothy T. Clark ◽  
Ye Zhou
Keyword(s):  
Flow Field ◽  
Power Law ◽  
Mixing Layer ◽  
Power Laws ◽  
Mixing Layers ◽  
Spatial Gradients ◽  
Power Law Exponent ◽  
Virtual Time ◽  
Time Origin ◽  
Density Ratios

The Richtmyer-Meshkov mixing layer is initiated by the passing of a shock over an interface between fluid of differing densities. The energy deposited during the shock passage undergoes a relaxation process during which the fluctuational energy in the flow field decays and the spatial gradients of the flow field decrease in time. This late stage of Richtmyer-Meshkov mixing layers is studied from the viewpoint of self-similarity. Analogies with weakly anisotropic turbulence suggest that both the bubble-side and spike-side widths of the mixing layer should evolve as power-laws in time, with the same power-law exponent and virtual time origin for both sides. The analogy also bounds the power-law exponent between 2∕7 and 1∕2. It is then shown that the assumption of identical power-law exponents for bubbles and spikes yields fits that are in good agreement with experiment at modest density ratios.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multi-trace Bayesian AVO petrophysics inversion in multi-porosity reservoirs

Geophysics ◽  
2021 ◽  
pp. 1-101
Author(s):  
Kun Li ◽  
Xingyao Yin ◽  
Zhaoyun Zong ◽  
Dario Grana
Keyword(s):  
Bulk Modulus ◽  
Pore Volume ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
Volume Fraction ◽  
Inversion Method ◽  
Reservoir Properties ◽  
Pore Volume Fraction ◽  
Pp Wave ◽  
Matrix Shear

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude variation with offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. Generally, PP-wave reflection coefficients, elastic moduli and petrophysical parameters are nonlinearly coupled, especially in the multiple type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We propose a new approach that combines Biot-Gassmann’s poro-elasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multi-trace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. The proposed stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of the proposed inversion method is illustrated with synthetic examples and a real data application.

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