scholarly journals Catalog of Coefficients for Estimating Bulk and Shear Moduli as a Function of Lithology

2021 ◽  
Vol 17 ◽  
pp. 162-167
Author(s):  
J.R. Fanchi ◽  
Keyword(s):  
Shear Moduli

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Soft Matter ◽  
2021 ◽  
Author(s):  
D. Zeb Rocklin ◽  
Lilian C Hsiao ◽  
Megan E Szakasits ◽  
Michael J Solomon ◽  
Xiaoming Mao
Keyword(s):  
Coordination Number ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Structural Heterogeneity ◽  
Colloidal Gels ◽  
Shear Moduli ◽  
Rheological Measurements

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number,...

scholarly journals Modelling the elastic mechanical properties of bioactive glass-derived scaffolds

2020 ◽  
Vol 6 (1) ◽  
pp. 50-56
Author(s):  
Francesco Baino ◽  
Elisa Fiume
Keyword(s):  
Elastic Properties ◽  
Poisson’S Ratio ◽  
Mechanical Performance ◽  
Solid Material ◽  
Poisson's Ratio ◽  
Predictive Capability ◽  
Shear Moduli ◽  
Wide Range ◽  
Constitutive Parameters ◽  
The Relationship

AbstractPorosity is known to play a pivotal role in dictating the functional properties of biomedical scaffolds, with special reference to mechanical performance. While compressive strength is relatively easy to be experimentally assessed even for brittle ceramic and glass foams, elastic properties are much more difficult to be reliably estimated. Therefore, describing and, hence, predicting the relationship between porosity and elastic properties based only on the constitutive parameters of the solid material is still a challenge. In this work, we quantitatively compare the predictive capability of a set of different models in describing, over a wide range of porosity, the elastic modulus (7 models), shear modulus (3 models) and Poisson’s ratio (7 models) of bioactive silicate glass-derived scaffolds produced by foam replication. For these types of biomedical materials, the porosity dependence of elastic and shear moduli follows a second-order power-law approximation, whereas the relationship between porosity and Poisson’s ratio is well fitted by a linear equation.

scholarly journals Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1450
Author(s):  
Yuri Vassilevski ◽  
Alexey Liogky ◽  
Victoria Salamatova
Keyword(s):  
Aortic Valve ◽  
Finite Elements ◽  
Shell Model ◽  
Thin Shell ◽  
Aortic Valves ◽  
Shear Moduli ◽  
Force Method ◽  
Elastic Potentials ◽  
Shell Analysis ◽  
First Time

Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone.

scholarly journals High-Temperature Elastic Properties of Yttrium-Doped Barium Zirconate

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 968
Author(s):  
Fumitada Iguchi ◽  
Keisuke Hinata
Keyword(s):  
High Temperature ◽  
Young’S Modulus ◽  
Elastic Properties ◽  
Measurement Method ◽  
Young's Modulus ◽  
Barium Zirconate ◽  
Shear Moduli ◽  
Ceramic Fuel ◽  
Yttrium Concentration ◽  
Ceramic Fuel Cells

The elastic properties of 0, 10, 15, and 20 mol% yttrium-doped barium zirconate (BZY0, BZY10, BZY15, and BZY20) at the operating temperatures of protonic ceramic fuel cells were evaluated. The proposed measurement method for low sinterability materials could accurately determine the sonic velocities of small-pellet-type samples, and the elastic properties were determined based on these velocities. The Young’s modulus of BZY10, BZY15, and BZY20 was 224, 218, and 209 GPa at 20 °C, respectively, and the values decreased as the yttrium concentration increased. At high temperatures (>20 °C), as the temperature increased, the Young’s and shear moduli decreased, whereas the bulk modulus and Poisson’s ratio increased. The Young’s and shear moduli varied nonlinearly with the temperature: The values decreased rapidly from 100 to 300 °C and gradually at temperatures beyond 400 °C. The Young’s modulus of BZY10, BZY15, and BZY20 was 137, 159, and 122 GPa at 500 °C, respectively, 30–40% smaller than the values at 20 °C. The influence of the temperature was larger than that of the change in the yttrium concentration.

scholarly journals Validation of Digital Rock Physics Algorithms

Minerals ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 669
Author(s):  
Rongrong Lin ◽  
Leon Thomsen
Keyword(s):  
Rock Physics ◽  
Image Resolution ◽  
Staggered Grid ◽  
Static Properties ◽  
Shear Moduli ◽  
Digital Rock Physics ◽  
Digital Rock ◽  
Saturated Rock ◽  
Theoretical Predictions ◽  
Theoretical Test

With a detailed microscopic image of a rock sample, one can determine the corresponding 3-D grain geometry, forming a basis to calculate the elastic properties numerically. The issues which arise in such a calculation include those associated with image resolution, the registration of the digital numerical grid with the digital image, and grain anisotropy. Further, there is a need to validate the numerical calculation via experiment or theory. Because of the geometrical complexity of the rock, the best theoretical test employs the Hashin–Shtrikman result that, for an aggregate of two isotropic components with equal shear moduli, the bulk modulus is uniquely determined, independent of the micro-geometry. Similarly, for an aggregate of two isotropic components with a certain combination of elastic moduli defined herein, the Hashin–Shtrikman formulae give a unique result for the shear modulus, independent of the micro-geometry. For a porous, saturated rock, the solid incompressibility may be calculated via an “unjacketed” test, independent of the micro-geometry. Any numerical algorithm proposed for digital rock physics computation should be validated by successfully confirming these theoretical predictions. Using these tests, we validate a previously published staggered-grid finite difference damped time-stepping algorithm to calculate the static properties of digital rock models.

scholarly journals Direct Measurement of the Area Expansion and Shear Moduli of the Human Red Blood Cell Membrane Skeleton

2001 ◽  
Vol 81 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Guillaume Lenormand ◽  
Sylvie Hénon ◽  
Alain Richert ◽  
Jacqueline Siméon ◽  
François Gallet
Keyword(s):  
Cell Membrane ◽  
Blood Cell ◽  
Direct Measurement ◽  
Red Blood Cell ◽  
Membrane Skeleton ◽  
Shear Moduli ◽  
Red Blood Cell Membrane ◽  
Area Expansion

Young’s and shear moduli of glued laminated timber composed of different species obtained by a flexural vibration test

Holzforschung ◽  
2012 ◽  
Vol 66 (7) ◽  
pp. 871-875 ◽  
Author(s):  
Yoshitaka Kubojima ◽  
Mario Tonosaki
Keyword(s):  
Elastic Constants ◽  
Pinus Densiflora ◽  
Flexural Vibration ◽  
Japanese Cedar ◽  
Picea Sitchensis ◽  
Vibration Test ◽  
Shear Moduli ◽  
Glued Laminated Timber ◽  
Flexural Vibration Test ◽  
Lamination Theory

Abstract The applicability of the flexural vibration test to determine the elastic constants of glued laminated timber (GLT) composed of five wood species (ash, Fraxinus spaethiana Lingelsh.; balsa, Ochroma pyramidale Urban.; Japanese cedar, Cryptomeria japonica D. Don; Japanese red pine, Pinus densiflora Sieb. et Zucc.; Sitka spruce, Picea sitchensis Carr.) has been investigated. GLT models were prepared from four laminae with dimensions of 30 (R)×5 (T)×300 (L) mm3. The suitability of Japanese cedar for inner layers in GLTs was tested by flexural vibration test to determine the elastic constants of the laminae and the glued laminated timber. The Young’s and shear moduli were calculated by the Goens-Hearmon regression method based on the Timoshenko theory of bending (TGH method), and the results were compared with the estimated values based on the Young’s and shear moduli measured individually of each lamina. The simple lamination theory was found to be applicable for Young’s modulus but not to shear modulus. The result obtained based on the lamination theory from the shear strain energy was similar to that obtained by the TGH method.

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