Constitutive equations for transversely isotropic elastic dielectrics with Schur's lemma

2001 ◽  
Vol 38 (48-49) ◽  
pp. 8773-8785
Author(s):  
K.L. Chowdhury
Keyword(s):  
Constitutive Equations ◽  
Transversely Isotropic ◽  
Schur’S Lemma ◽  
Schur's Lemma

scholarly journals A Remark on the Orthogonality Relations in the Representation Theory of Finite Groups

1959 ◽  
Vol 11 ◽  
pp. 59-60 ◽  
Author(s):  
Hirosi Nagao
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Representation Theory ◽  
Finite Groups ◽  
Characteristic Zero ◽  
Orthogonality Relations ◽  
Schur’S Lemma ◽  
Image Position ◽  
A Finite Group ◽  
Schur's Lemma

Let G be a finite group of order g, andbe an absolutely irreducible representation of degree fμ over a field of characteristic zero. As is well known, by using Schur's lemma (1), we can prove the following orthogonality relations for the coefficients :1It is easy to conclude from (1) the following orthogonality relations for characters:whereand is 1 or 0 according as t and s are conjugate in G or not, and n(t) is the order of the normalize of t.

scholarly journals Family Symmetries and Multi Higgs Doublet Models

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 156
Author(s):  
Bartosz Dziewit ◽  
Jacek Holeczek ◽  
Sebastian Zając ◽  
Marek Zrałek
Keyword(s):  
Standard Model ◽  
Higgs Doublet ◽  
Family Symmetry ◽  
The Standard Model ◽  
Schur’S Lemma ◽  
Finite Subgroups ◽  
Free Parameters ◽  
Schur's Lemma

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the U ( 3 ) group up to the order of 1025.

Non-Linear Constitutive Equations for Transversely Isotropic Materials Belonging to the С∞ and С∞h Symmetry Groups

2019 ◽  
pp. 46-59
Author(s):  
S.V. Tsvetkov
Keyword(s):  
Constitutive Equations ◽  
Infinite Order ◽  
Transversely Isotropic ◽  
Material Structure ◽  
Symmetry Groups ◽  
Tensor Function ◽  
Symmetry Principle ◽  
Isotropic Materials ◽  
Irreducible Form ◽  
Transversely Isotropic Materials

Transversely isotropic materials feature infinite-order symmetry axes. Depending on which other symmetry elements are found in the material structure, five symmetry groups may be distinguished among transversely isotropic materials. We consider constitutive equations for these materials. These equations connect two symmetric second-order tensors. Two types of constitutive equations describe the properties of these five material groups. We derived constitutive equations for materials belonging to the C∞ and C∞h symmetry groups in the tensor function form. To do this, we used corollaries of Curie's Symmetry Principle. This makes it possible to obtain a fully irreducible form of the tensor function.

ANCF Analysis of Textile Systems

2015 ◽  
Vol 11 (3) ◽  
Author(s):  
Liang Wang ◽  
Yongxing Wang ◽  
Antonio M. Recuero ◽  
Ahmed A. Shabana
Keyword(s):  
Constitutive Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Transversely Isotropic ◽  
Textile Material ◽  
Deformation Tensor ◽  
Material Forces ◽  
Isotropic Component ◽  
Filament Bundles

This paper presents a new flexible multibody system (MBS) approach for modeling textile systems including roll-drafting sets used in chemical textile machinery. The proposed approach can be used in the analysis of textile materials such as lubricated polyester filament bundles (PFBs), which have uncommon material properties best described by specialized continuum mechanics constitutive models. In this investigation, the absolute nodal coordinate formulation (ANCF) is used to model PFB as a hyperelastic transversely isotropic material. The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy–Green deformation tensor. Using this energy decomposition, the second Piola–Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. The constitutive equations are used to define the generalized material forces associated with the coordinates of three-dimensional fully parameterized ANCF finite elements (FEs). The proposed approach allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to describe the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between the rollers and PFB.

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