A Spherical Model Calculation for Volumetric Response of Porous Rocks

1975 ◽  
Vol 42 (2) ◽  
pp. 363-368 ◽  
Author(s):  
J. J. Bhatt ◽  
M. M. Carroll ◽  
J. F. Schatz
Keyword(s):  
Experimental Data ◽  
Model Calculation ◽  
Hollow Sphere ◽  
Constitutive Relations ◽  
Applied Pressure ◽  
Spherical Model ◽  
Incompressible Material ◽  
Porous Rocks ◽  
Theoretical Predictions ◽  
Volumetric Response

The problem of external pressurization and release is solved for a hollow sphere of incompressible material obeying Coulomb’s law of failure. The resulting relations between the applied pressure and the porosity of the sphere are used in formulating constitutive relations for the volumetric response of porous rocks. The theoretical predictions are compared with experimental data for a sandstone and a tuff.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals An Additive Model to Predict the Rheological and Mechanical Properties of Polypropylene Blends Made by Virgin and Reprocessed Components

Recycling ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 2
Author(s):  
Francesco Paolo La Mantia ◽  
Maria Chiara Mistretta ◽  
Vincenzo Titone
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Additive Model ◽  
Industrial Process ◽  
Theoretical Predictions ◽  
Experimental Values ◽  
Polypropylene Blends ◽  
Polypropylene Sample

In this work, an additive model for the prediction of the rheological and mechanical properties of monopolymer blends made by virgin and reprocessed components is proposed. A polypropylene sample has been reprocessed more times in an extruder and monopolymer blends have been prepared by simulating an industrial process. The scraps are exposed to regrinding and are melt reprocessed before mixing with the virgin polymer. The reprocessed polymer is, then, subjected to some thermomechanical degradation. Rheological and mechanical experimental data have been compared with the theoretical predictions. The results obtained showed that the values of this simple additive model are a very good fit for the experimental values of both rheological and mechanical properties.

A Technique for the Laboratory Determination of Recirculation in Single Needle Dialysis

1993 ◽  
Vol 16 (2) ◽  
pp. 63-70 ◽  
Author(s):  
N.A. Hoenich ◽  
P.T. Smirthwaite ◽  
C. Woffindin ◽  
P. Lancaster ◽  
T.H. Frost ◽  
...  
Keyword(s):  
Experimental Data ◽  
Flow Rate ◽  
Experimental Results ◽  
New Technique ◽  
Treatment Efficiency ◽  
Single Lumen ◽  
Theoretical Predictions ◽  
Lumen Catheter ◽  
A New Technique

Recirculation is an important factor in single needle dialysis and, if high, can compromise treatment efficiency. To provide information regarding recirculation characteristics of access devices used in single needle dialysis, we have developed a new technique to characterise recirculation and have used this to measure the recirculation of a Terumo 15G fistula needle and a VasCath SC2300 single lumen catheter. The experimentally obtained results agreed well with those established clinically (8.5 ± 2.4% and 18.4 ± 3.4%). The experimental results have also demonstrated a dependence on access type, pump speeds and fistula flow rate. A comparison of experimental data with theoretical predictions showed that the latter exceeded those measured with the largest contribution being due to the experimental fistula.

Systematic ab initio study of the compressibility of silicate garnets

2001 ◽  
Vol 57 (2) ◽  
pp. 163-177 ◽  
Author(s):  
V. Milman ◽  
E. V. Akhmatskaya ◽  
R. H. Nobes ◽  
B. Winkler ◽  
C. J. Pickard ◽  
...  
Keyword(s):  
Experimental Data ◽  
Density Functional ◽  
Structural Parameters ◽  
Applied Pressure ◽  
Basis Set ◽  
Ionic Radii ◽  
Cell Parameters ◽  
The Density Functional Theory ◽  
Dodecahedral Site ◽  
Compression Mechanism

The structural properties of the silicate garnets andradite, Ca3Fe2Si3O12, uvarovite, Ca3Cr2Si3O12, knorringite, Mg3Cr2Si3O12, goldmanite, Ca3V2Si3O12, blythite, Mn^{2+}_3Mn^{3+}_2Si3O12, skiagite, Fe^{2+}_3Fe^{3+}_2Si3O12, calderite, Mn^{2+}_3Fe^{3+}_2Si3O12, and khoharite, Mg3Fe^{3+}_2Si3O12, have been investigated with a quantum-mechanical model as a function of applied pressure. The study has been performed with the density functional theory code CASTEP, which uses pseudopotentials and a plane-wave basis set. All structural parameters have been optimized. The calculated static geometries (cell parameters, internal coordinates of atoms and bond lengths), bulk moduli and their pressure derivatives are in good agreement with the experimental data available. Predictions are made for those cases where no experimental data have been reported. The data clearly indicate that the elastic properties of all silicate garnets are dominated by the compressibility of the dodecahedral site. The compression mechanism is found to be based on a bending of the angle between the centers of the SiO4 tetrahedra and the adjacent octahedra, as in the aluminosilicate garnets. An analysis of the relationship between ionic radii of the cations and the compressibility of silicate garnets is presented.

Wilberforce pendulum: modelling linearly damped coupled oscillations of a spring-mass system

2021 ◽  
Author(s):  
Robert Frederik Diaz Uy ◽  
Chenghao Yuan ◽  
Zhengshan Chai ◽  
Justin Khor
Keyword(s):  
Experimental Data ◽  
Angular Displacement ◽  
Beat Frequency ◽  
Vertical Displacement ◽  
Quantitative Model ◽  
Moment Of Inertia ◽  
Lagrangian Formalism ◽  
Mass System ◽  
Coupled Oscillations ◽  
Theoretical Predictions

Abstract The Wilberforce pendulum is a coupled spring-mass system, where a mass with adjustable moment of inertia is suspended from a helical spring. Energy is converted between the translational and torsional modes, and this energy conversion is most clearly observed at resonance, which occurs when the damped natural frequencies of the two oscillation modes are equal. A theoretical model—with energy losses due to viscous damping accounted for—was formulated using the Lagrangian formalism to predict the pendulum mass’ trajectory. Theoretical predictions were compared with experimental data, showing good agreement. Fourier analysis of both theoretical predictions and experimental data further corroborate the validity of our quantitative model. The dependence of oscillation features like beat frequency and maximum conversion amplitude on relevant parameters such as the initial vertical displacement, initial angular displacement and moment of inertia was also investigated and experimentally verified.

Finite elasticity of elastomeric materials

2020 ◽  
pp. 637-654
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Free Energy ◽  
Constitutive Relations ◽  
Finite Elasticity ◽  
Energy Functions ◽  
Slightly Compressible ◽  
Elastomeric Materials ◽  
Volumetric Response

This chapter presents several technologically important constitutive relations for elastomeric materials. In particular, the Neo-Hookean, Mooney-Rivlin, Ogden, Arruda-Boyce, and Gent free energy functions are discussed in the context of incompressible response. Extensions to the slightly compressible case are also detailed, this includes a presentation of a number of possible volumetric response relations and their properties.

scholarly journals Bioinspired aerofoil adaptations: the next steps for theoretical models

2019 ◽  
Vol 377 (2159) ◽  
pp. 20190070 ◽  
Author(s):  
Lorna J. Ayton
Keyword(s):  
Experimental Data ◽  
Theoretical Models ◽  
Theoretical Modelling ◽  
Experimental Measurements ◽  
Far Field ◽  
Acoustic Analogy ◽  
Trailing Edge ◽  
Trailing Edge Noise ◽  
Theoretical Predictions ◽  
Field Noise

The extended introduction in this paper reviews the theoretical modelling of leading- and trailing-edge noise, various bioinspired aerofoil adaptations to both the leading and trailing edges of blades, and how these adaptations aid in the reduction of aerofoil–turbulence interaction noise. Attention is given to the agreement between current theoretical predictions and experimental measurements, in particular, for turbulent interactions at the trailing edge of an aerofoil. Where there is a poor agreement between theoretical models and experimental data the features neglected from the theoretical models are discussed. Notably, it is known that theoretical predictions for porous trailing-edge adaptations do not agree well with experimental measurements. Previous works propose the reason for this: theoretical models do not account for surface roughness due to the porous material and thus omit a key noise source. The remainder of this paper, therefore, presents an analytical model, based upon the acoustic analogy, to predict the far-field noise due to a rough surface at the trailing edge of an aerofoil. Unlike previous roughness noise models which focus on roughness over an infinite wall, the model presented here includes diffraction by a sharp edge. The new results are seen to be in better agreement with experimental data than previous models which neglect diffraction by an edge. This new model could then be used to improve theoretical predictions for far-field noise generated by turbulent interactions with a (rough) porous trailing edge. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

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