A General Method for Data Averaging of Anisotropic Elastic Constants

1993 ◽  
Vol 60 (3) ◽  
pp. 614-618 ◽  
Author(s):  
M. Gre´diac ◽  
A. Vautrin ◽  
G. Verchery
Keyword(s):  
Experimental Data ◽  
Elastic Constants ◽  
Bending Tests ◽  
Compliance Tensor ◽  
Best Value ◽  
Anisotropic Elastic ◽  
Experimental Scatter ◽  
General Method

Redundant experimental data are usually required to determine the best value for the whole set of compliances of an anisotropic laminate. A method is presented here to optimize the compliance tensor values using the five invariants of fourth-rank compliance tensors. A vectorial representation of those invariants is given. It provides a compact presentation of the data and reveals the experimental scatter. Experimental data obtained with bending tests on plates are used as an example to optimize the flexural compliance tensor of a laminate and to show the relevance of the method in practice.

INVERSION OF ANISOTROPIC ELASTIC CONSTANTS AND MUD SPEED USING BOREHOLE SONIC MODES

2020 ◽  
Author(s):  
Ting Lei ◽  
◽  
Romain Prioul ◽  
Adam Donald ◽  
Edgar Ignacio Velez Arteaga ◽  
...  
Keyword(s):  
Elastic Constants ◽  
Anisotropic Elastic

Representation of the Microstructural Dependence of the Anisotropic Elastic Constants of Textured Materials

1990 ◽  
Vol 207 ◽  
Author(s):  
Stephen C. Cowin
Keyword(s):  
Elastic Constants ◽  
Material Symmetry ◽  
Hooke’S Law ◽  
Mechanical Models ◽  
Hooke's Law ◽  
Micromechanical Models ◽  
Anisotropic Elastic ◽  
Anisotropic Form ◽  
Textured Materials ◽  
Elastic Coefficients

AbstractThis paper addresses the question of representing the dependence of the elastic coefficients in the anisotropic form of Hooke's law upon the microstructure of a material. The concern is with textured material symmetries, that is to say materials such as natural and man-made composites whose material symmetry is determined by microstructural organization. The approach is to relate the anisotropic elastic coefficients to local geometric or stereological measures of the microstructure. The predictions of micromechanical models and continuum mechanical models are compared and are found to be consistent with each other.

The elastic field outside an ellipsoidal inclusion

1959 ◽  
Vol 252 (1271) ◽  
pp. 561-569 ◽  
Keyword(s):  
Velocity Field ◽  
Viscous Fluid ◽  
Elastic Constants ◽  
Strain Energy ◽  
Elastic Field ◽  
Ellipsoidal Inclusion ◽  
Harmonic Potential ◽  
Surface Distribution ◽  
Shear Transformation ◽  
General Method

The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a certain surface distribution may be used in place of the biharmonic potential used previously. The elastic field outside an ellipsoidal inclusion or inhomogeneity may be expressed entirely in terms of the harmonic potential of a solid ellipsoid. The solution gives incidentally the velocity field about an ellipsoid which is deforming homogeneously in a viscous fluid. An expression given previously for the strain energy of an ellipsoidal region which has undergone a shear transformation is generalized to the case where the region has elastic constants different from those of its surroundings. The Appendix outlines a general method of calculating biharmonic potentials.

The physical properties of ThCr2Si2-type superconductors MPd2P2 (M = Y, La): A theoretical investigation

2018 ◽  
Vol 32 (28) ◽  
pp. 1850312
Author(s):  
Md. Lokman Ali ◽  
Md. Tosaddek Hossen ◽  
Shahin Alam ◽  
Md. Sadek Hossain ◽  
Jakiul Islam ◽  
...  
Keyword(s):  
Experimental Data ◽  
Elastic Constants ◽  
Structural Data ◽  
Computer Code ◽  
Generalized Gradient ◽  
Generalized Gradient Approximation ◽  
Anisotropic Factor ◽  
Optical Functions ◽  
Debye Temperatures ◽  
Ductile Behavior

The structural stability, elastic, mechanical, optical characteristics and Debye temperature of single crystalline superconductors MPd2P2 (M = Y, La) were investigated by using the ab initio technique. We have carried out the plane wave pseudopotential within the generalized gradient approximation (GGA) implemented in the CASTEP computer code. Our investigated results of structural data are in well consistent with the previous experimental data. The bulk modulus B, shear modulus G, Young’s modulus E, Poisson’s ratio v, hardness H, and anisotropic factor A of MPd2P2 (M = Y, La) compounds were evaluated from the calculated elastic constants. The analysis of ratio B/G shows that the MPd2P2 superconductors are in ductile behavior. The Debye temperatures are also investigated from the elastic constants. Finally, the optical functions including reflectivity, absorption coefficient, loss function, conductivity, refractive index, dielectric function are calculated and analyzed.

scholarly journals Research on MRD Parametric Model Based on Magic Formula

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Pan ◽  
Zhengtao Yan ◽  
Jingjun Lou ◽  
Shijian Zhu
Keyword(s):  
Experimental Data ◽  
Working Conditions ◽  
Parametric Model ◽  
Parametric Modelling ◽  
Loop Model ◽  
Magnetorheological Dampers ◽  
Nonlinear Characteristics ◽  
Magic Formula ◽  
Parameterized Model ◽  
General Method

In order to get a better description to the nonlinear characteristics of magnetorheological dampers, the magic formula is introduced into the general method of parametric modelling of magnetorheological dampers to propose a new parameterized model called magic formula-hysteresis loop model (MFM). The new model is simple in structure, the physical meaning of each parameter is clear, and the parameter identification is convenient. The fitting and experimental data of MFM and the phenomenon model under different conditions are applied for error analysis and comparison. The results show that the errors of MFM are more accurate and have better fitting and experimental data under different working conditions, which also have better adaptability and versatility.

scholarly journals Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

2021 ◽  
Author(s):  
Christoph Oefner ◽  
Elena Riemer ◽  
Kerstin Funke ◽  
Michael Werner ◽  
Christoph-Eckhard Heyde ◽  
...  
Keyword(s):  
Finite Element ◽  
Lumbar Spine ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Bone Volume ◽  
Human Bone ◽  
Homogenization Theory ◽  
Elastic Parameters ◽  
Anisotropic Elastic

AbstractIn biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).

scholarly journals Measurement of the Anisotropic Dynamic Elastic Constants of Additive Manufactured and Wrought Ti6Al4V Alloys

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 638
Author(s):  
Ofer Tevet ◽  
David Svetlizky ◽  
David Harel ◽  
Zahava Barkay ◽  
Dolev Geva ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Elastic Constants ◽  
Electron Backscatter Diffraction ◽  
Mechanical Design ◽  
Rolling Direction ◽  
Micro Computed Tomography ◽  
Phase Layer ◽  
Anisotropic Elastic ◽  
Hot Rolled ◽  
Pulse Echo

Additively manufactured (AM) materials and hot rolled materials are typically orthotropic, and exhibit anisotropic elastic properties. This paper elucidates the anisotropic elastic properties (Young’s modulus, shear modulus, and Poisson’s ratio) of Ti6Al4V alloy in four different conditions: three AM (by selective laser melting, SLM, electron beam melting, EBM, and directed energy deposition, DED, processes) and one wrought alloy (for comparison). A specially designed polygon sample allowed measurement of 12 sound wave velocities (SWVs), employing the dynamic pulse-echo ultrasonic technique. In conjunction with the measured density values, these SWVs enabled deriving of the tensor of elastic constants (Cij) and the three-dimensional (3D) Young’s moduli maps. Electron backscatter diffraction (EBSD) and micro-computed tomography (μCT) were employed to characterize the grain size and orientation as well as porosity and other defects which could explain the difference in the measured elastic constants of the four materials. All three types of AM materials showed only minor anisotropy. The wrought (hot rolled) alloy exhibited the highest density, virtually pore-free μCT images, and the highest ultrasonic anisotropy and polarity behavior. EBSD analysis revealed that a thin β-phase layer that formed along the elongated grain boundaries caused the ultrasonic polarity behavior. The finding that the elastic properties depend on the manufacturing process and on the angle relative to either the rolling direction or the AM build direction should be taken into account in the design of products. The data reported herein is valuable for materials selection and finite element analyses in mechanical design. The pulse-echo measurement procedure employed in this study may be further adapted and used for quality control of AM materials and parts.

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