scholarly journals Discussion: “Saint-Venant’s Principle and End Effects in Anisotropic Elasticity” (Choi, I., and Horgan, C. O., 1977, ASME J. Appl. Mech., 44, pp. 424–430)

1978 ◽  
Vol 45 (2) ◽  
pp. 455-455
Author(s):  
T. Leko
Keyword(s):  
Anisotropic Elasticity ◽  
End Effects

Saint-Venant’s Principle and End Effects in Anisotropic Elasticity

1977 ◽  
Vol 44 (3) ◽  
pp. 424-430 ◽  
Author(s):  
I. Choi ◽  
C. O. Horgan
Keyword(s):  
Isotropic Material ◽  
Epoxy Composite ◽  
Transversely Isotropic ◽  
Anisotropic Elasticity ◽  
Decay Length ◽  
End Effects ◽  
Slow Decay ◽  
Rectangular Strip ◽  
Elasticity Problems ◽  
Transversely Isotropic Materials

The purpose of this paper is to draw attention to the fact that the routine application of Saint-Venant’s principle in the solution of elasticity problems involving highly anisotropic or composite materials is not justified in general. This is illustrated in the context of the plane problem of elasticity for an anisotropic rectangular strip loaded only on the short ends. For highly anisotropic transversely isotropic materials, the slow decay of end effects is demonstrated using a method involving self-equilibrating eigenfunctions. For a graphite/epoxy composite, for example, the characteristic decay length is shown to be approximately four times that for an isotropic material. The results have implications in the accurate measurement of mechanical properties of anisotropic materials.

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

scholarly journals A Novel, Improved Equivalent Circuit Model for Double-Sided Linear Induction Motor

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1644
Author(s):  
Qian Zhang ◽  
Huijuan Liu ◽  
Tengfei Song ◽  
Zhenyang Zhang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Equivalent Circuit ◽  
Skin Effect ◽  
Equivalent Circuit Model ◽  
Element Model ◽  
Circuit Model ◽  
End Effects ◽  
3D Finite Element ◽  
Linear Induction

A novel, improved equivalent circuit model of double-sided linear induction motors (DLIMs) is proposed, which takes the skin effect and the nonzero leakage reactance of the secondary, longitudinal, and transverse end effects into consideration. Firstly, the traditional equivalent circuit with longitudinal and transverse end effects are briefly reviewed. Additionally, the correction coefficients for longitudinal and transverse end effects derived by one-dimensional analysis models are given. Secondly, correction factors for skin effect, which reflects the inhomogeneous air gap magnetic field vertically, and the secondary leakage reactance are derived by the quasi-two-dimensional analysis model. Then, the proposed equivalent circuit is presented, and the excitation reactance and secondary resistance are modified by the correction coefficients derived from the three analytical models. Finally, a three-dimensional (3D) finite element model is used to verify the proposed equivalent circuit model under varying air gap width and frequency, and the results are also compared with that of the traditional equivalent circuit models. The calculated thrust characteristics by the proposed equivalent circuit and 3D finite element model are experimentally validated under a constant voltage–frequency drive.

scholarly journals Viscoelastic phase-field fracture using the framework of representative crack elements

2021 ◽  
Author(s):  
Bo Yin ◽  
Johannes Storm ◽  
Michael Kaliske
Keyword(s):  
Phase Field ◽  
Consistency Condition ◽  
Field Method ◽  
Anisotropic Elasticity ◽  
Phase Field Method ◽  
Internal Variables ◽  
Crack Model ◽  
Material Degradation ◽  
Discrete Crack ◽  
Deformation State

AbstractThe promising phase-field method has been intensively studied for crack approximation in brittle materials. The realistic representation of material degradation at a fully evolved crack is still one of the main challenges. Several energy split formulations have been postulated to describe the crack evolution physically. A recent approach based on the concept of representative crack elements (RCE) in Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) introduces a variational framework to derive the kinematically consistent material degradation. The realistic material degradation is further tested using the self-consistency condition, which is particularly compared to a discrete crack model. This work extends the brittle RCE phase-field modeling towards rate-dependent fracture evolution in a viscoelastic continuum. The novelty of this paper is taking internal variables due to viscoelasticity into account to determine the crack deformation state. Meanwhile, a transient extension from Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) is also considered. The model is derived thermodynamic-consistently and implemented into the FE framework. Several representative numerical examples are investigated, and consequently, the according findings and potential perspectives are discussed to close this paper.

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