General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids

1995 ◽  
Vol 39 (1) ◽  
pp. 47-73 ◽  
Author(s):  
H. Xiao
Keyword(s):  
Constitutive Equations ◽  
Transversely Isotropic ◽  
Irreducible Representations ◽  
Elastic Solids ◽  
Elastic Crystals

Cracks in Transversely Isotropic and Inhomogeneous Elastic Solids

2014 ◽  
pp. 791-798
Author(s):  
Ernian Pan ◽  
Chunying Dong ◽  
Ali Sangghaleh ◽  
Yanfei Zhao
Keyword(s):  
Transversely Isotropic ◽  
Elastic Solids

scholarly journals The JKR-type adhesive contact problems for transversely isotropic elastic solids

2014 ◽  
Vol 75 ◽  
pp. 34-44 ◽  
Author(s):  
Feodor M. Borodich ◽  
Boris A. Galanov ◽  
Leon M. Keer ◽  
Maria M. Suarez-Alvarez
Keyword(s):  
Transversely Isotropic ◽  
Contact Problems ◽  
Adhesive Contact ◽  
Elastic Solids

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.

scholarly journals Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids

1975 ◽  
Vol 19 (1) ◽  
pp. 40-54 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Existence Of Solutions ◽  
Lateral Displacement ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Elastic Solids ◽  
Standard Potential ◽  
Linear Elastic ◽  
Axis Of Symmetry ◽  
Uniqueness And Existence ◽  
Traction Boundary Conditions

AbstractA plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.

Theory of Representations for Tensor Functions—A Unified Invariant Approach to Constitutive Equations

1994 ◽  
Vol 47 (11) ◽  
pp. 545-587 ◽  
Author(s):  
Q.-S. Zheng
Keyword(s):  
Mechanical Behavior ◽  
Constitutive Equations ◽  
Constitutive Laws ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Applied Mechanics ◽  
Invariant Formulation ◽  
Physical Spaces ◽  
Anisotropic Tensor ◽  
Invariant Approach

Representations in complete and irreducible forms for tensor functions allow general consistent invariant forms of the nonlinear constitutive equations and specify the number and type of the scalar variables involved. They have proved to be even more pertinent in attempts to model mechanical behavior of anisotropic materials, since here invariant conditions predominate and the number and type of independent scalar variables cannot be found by simple arguments. In the last few years, the theory of representations for tensor functions has been well established, including three fundamental principles, a number of essential theorems and a large amount of complete and irreducible representations for both isotropic and anisotropic tensor functions in three- and two-dimensional physical spaces. The objective of the present monograph is to summarize and recapitulate the up-to-date developments and results in the theory of representations for tensor functions for the convenience of further applications in contemporary applied mechanics. Some general topics on unified invariant formulation of constitutive laws are investigated.

scholarly journals Stress field formulation of linear electro-magneto-elastic materials

2019 ◽  
Vol 24 (12) ◽  
pp. 3806-3822
Author(s):  
A Amiri-Hezaveh ◽  
P Karimi ◽  
M Ostoja-Starzewski
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Governing Equations ◽  
Field Equations ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Sufficient Set

A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

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