Procedure of the Galerkin Representation in Transversely Isotropic Elasticity

2018 ◽  
pp. 117-124 ◽  
Author(s):  
Dimitri V. Georgievskii
Keyword(s):  
Transversely Isotropic ◽  
Isotropic Elasticity

Development of Representative Volume Element Homogenization Model for Predicting Transversely Isotropic Elasticity of Lithium-Ion Batteries

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Jin Chul Yun ◽  
Seong Jin Park
Keyword(s):  
Representative Volume Element ◽  
Lithium Ion ◽  
Transversely Isotropic ◽  
Volume Element ◽  
Elastic Behavior ◽  
Design Stage ◽  
Design Parameters ◽  
Concept Design ◽  
Representative Volume ◽  
Isotropic Elasticity

In this study, a representative volume element (RVE) homogenization approach is proposed to predict the mechanical properties of a lithium-ion battery (LIB) cell, module, and pack in an electric vehicle (EV). Different RVE models for the LIB jellyroll and module are suggested. Various elastic properties obtained from RVE analyses were compared to the analytic solution. To validate the approach suggested, the elastic responses of two types of homogenized LIB module for various loading cases were compared to the model where all the jellyroll and module components were described fully. Additionally, parametric studies were conducted to determine the relationship between design parameters of the jellyroll components and the elastic behavior of LIB jellyroll and module. The results obtained in this study provide useful information for both LIB cell developers, at the concept design stage, and engineers of electric vehicles who want to predict the mechanical safety of a battery pack.

scholarly journals Transversely Isotropic Elasticity Imaging of Cancellous Bone

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Spencer W. Shore ◽  
Paul E. Barbone ◽  
Assad A. Oberai ◽  
Elise F. Morgan
Keyword(s):  
Mechanical Properties ◽  
Inverse Problem ◽  
Cancellous Bone ◽  
Material Properties ◽  
Transversely Isotropic ◽  
Elasticity Imaging ◽  
Elastic Parameters ◽  
Displacement Fields ◽  
Isotropic Materials ◽  
Isotropic Elasticity

To measure spatial variations in mechanical properties of biological materials, prior studies have typically performed mechanical tests on excised specimens of tissue. Less invasive measurements, however, are preferable in many applications, such as patient-specific modeling, disease diagnosis, and tracking of age- or damage-related degradation of mechanical properties. Elasticity imaging (elastography) is a nondestructive imaging method in which the distribution of elastic properties throughout a specimen can be reconstructed from measured strain or displacement fields. To date, most work in elasticity imaging has concerned incompressible, isotropic materials. This study presents an extension of elasticity imaging to three-dimensional, compressible, transversely isotropic materials. The formulation and solution of an inverse problem for an anisotropic tissue subjected to a combination of quasi-static loads is described, and an optimization and regularization strategy that indirectly obtains the solution to the inverse problem is presented. Several applications of transversely isotropic elasticity imaging to cancellous bone from the human vertebra are then considered. The feasibility of using isotropic elasticity imaging to obtain meaningful reconstructions of the distribution of material properties for vertebral cancellous bone from experiment is established. However, using simulation, it is shown that an isotropic reconstruction is not appropriate for anisotropic materials. It is further shown that the transversely isotropic method identifies a solution that predicts the measured displacements, reveals regions of low stiffness, and recovers all five elastic parameters with approximately 10% error. The recovery of a given elastic parameter is found to require the presence of its corresponding strain (e.g., a deformation that generates ɛ12 is necessary to reconstruct C1212), and the application of regularization is shown to improve accuracy. Finally, the effects of noise on reconstruction quality is demonstrated and a signal-to-noise ratio (SNR) of 40dB is identified as a reasonable threshold for obtaining accurate reconstructions from experimental data. This study demonstrates that given an appropriate set of displacement fields, level of regularization, and signal strength, the transversely isotropic method can recover the relative magnitudes of all five elastic parameters without an independent measurement of stress. The quality of the reconstructions improves with increasing contrast, magnitude of deformation, and asymmetry in the distributions of material properties, indicating that elasticity imaging of cancellous bone could be a useful tool in laboratory studies to monitor the progression of damage and disease in this tissue.

Analysis of Properties of Fiber Composites With Anisotropic Constituents

1979 ◽  
Vol 46 (3) ◽  
pp. 543-550 ◽  
Author(s):  
Z. Hashin
Keyword(s):  
Elastic Moduli ◽  
Fiber Composite ◽  
General Theorem ◽  
Transversely Isotropic ◽  
Dielectric Constants ◽  
Thermal Expansion Coefficients ◽  
Elasticity Equations ◽  
Isotropic Elasticity ◽  
Graphite Fibers ◽  
Effective Thermal Expansion

Expressions and bounds for the five effective elastic moduli of a unidirectional fiber composite, consisting of transversely isotropic fibers and matrix, are derived on the basis of analogies between isotropic and transversely isotropic elasticity equations. Application of results for determination of the five elastic moduli of graphite fibers is discussed. Effective thermal expansion coefficients are derived on the basis of a general theorem. Effective conductivities, dielectric constants, and magnetic permeabilities are derived by use of certain mathematical analogies.

On Obtaining Effective Transversely Isotropic Elasticity Tensors

2008 ◽  
Vol 94 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Mikhail Kochetov ◽  
Michael A. Slawinski
Keyword(s):  
Transversely Isotropic ◽  
Isotropic Elasticity ◽  
Elasticity Tensors

Transversely isotropic elasticity tensors

1987 ◽  
Vol 411 (1840) ◽  
pp. 85-93 ◽  
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Representation Formula ◽  
Elasticity Tensor ◽  
Transversely Isotropic Material ◽  
Hyperelastic Materials ◽  
Isotropic Elasticity ◽  
Elasticity Tensors ◽  
Symmetry Transformations ◽  
Axis Of Symmetry

A representation formula for the elasticity tensor of a linearly elastic, transversely isotropic material is obtained, depending on eight constants. If, besides rotations about the axis of symmetry, reflections with respect to planes through that axis are also regarded as admissible symmetry transformations for the material, it is shown that the number of constants reduces to six. It is also shown that, no matter whether reflections belong to the collection of admitted symmetry transformations or not, only five constants are needed for hyperelastic materials.

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