Thermal Elastic Constitutive Equation of Orthotropic Materials

2017 ◽  
Vol 863 ◽  
pp. 93-101
Author(s):  
Chen Li ◽  
Hai Ren Wang ◽  
Yan An Miao ◽  
Li Zhao
Keyword(s):  
Constitutive Equation ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Representation Theorem ◽  
Constitutive Equations ◽  
Orthotropic Materials ◽  
Tensor Function ◽  
Tensor Method ◽  
Scalar Invariant ◽  
Depth Study

In the finite deformation range, the numbers of orthotropic 2n order elastic constants are studied on the basis of tensor function and of its representation theorem. On the basis of elastic constant research, the elastic orthotropic constitutive equation is derived by using the tensor method. Based on orthotropic elastic constitutive equations an in-depth study on the constitutive theory of orthotropic nonlinear thermal elasticity is carried out, and by considering the deformation produced by the coupling of temperature and load, nonlinear orthotropic thermoelastic constitutive equation is further derived with representation of the tensor invariant and scalar invariant. The constitutive equations could be used very convenient to the application in reality.

Nonlinear Constitutive Equation and Elastic Constant of Rubber Material

2011 ◽  
Vol 415-417 ◽  
pp. 2267-2274 ◽  
Author(s):  
Chen Li ◽  
Li Zhao
Keyword(s):  
Constitutive Equation ◽  
Elastic Constants ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Compressible Material ◽  
Experiment Data ◽  
Rubber Material ◽  
Nonlinear Constitutive Equation ◽  
Depth Study ◽  
Material Constitutive Equation

In-depth study of compressible material constitutive equation, using incompressible condition, the nonlinear incompressible elastic solid’s complete irreducible constitutive equation and strain energy function expressed in invariants are derived in this essay. The elastic constants of rubber material are given by fitting the experiment data that was carried out by Treloar with the equation. Then we got evelen exact value of the elastic constants.

Effective Elastic Constants of Fiber-Eutectics and Transformation Particles Composite Ceramic

2010 ◽  
Vol 177 ◽  
pp. 182-185 ◽  
Author(s):  
Bao Feng Li ◽  
Jian Zheng ◽  
Xin Hua Ni ◽  
Ying Chen Ma ◽  
Jing Zhang
Keyword(s):  
Elastic Modulus ◽  
Elastic Constant ◽  
Effective Stress ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Composite Ceramic ◽  
Phase Model ◽  
Composite Ceramics ◽  
Effective Elastic Constants

The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

scholarly journals Extremely small twist elastic constants in lyotropic nematic liquid crystals

2020 ◽  
Vol 117 (44) ◽  
pp. 27238-27244 ◽  
Author(s):  
Clarissa F. Dietrich ◽  
Peter J. Collings ◽  
Thomas Sottmann ◽  
Per Rudquist ◽  
Frank Giesselmann
Keyword(s):  
Liquid Crystals ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Nematic Phase ◽  
Elastic Moduli ◽  
Building Blocks ◽  
Lyotropic Liquid Crystals ◽  
Order Of Magnitude ◽  
Typical Range ◽  
Special Case

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

scholarly journals High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy

2019 ◽  
Vol 38 (2019) ◽  
pp. 168-177 ◽  
Author(s):  
Liu Shi-feng ◽  
Shi Jia-min ◽  
Yang Xiao-kang ◽  
Cai Jun ◽  
Wang Qing-juan
Keyword(s):  
Titanium Alloy ◽  
High Temperature ◽  
Constitutive Equation ◽  
Constitutive Equations ◽  
Deformation Behaviour ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Compression Tests ◽  
Average Absolute Relative Error ◽  
Wide Range

AbstractIn this study, the high-temperature deformation behaviour of a TC17 titanium alloy was investigated by isothermal hot compression tests in a wide range of temperatures (973–1223 K) and strain rates (0.001–10 s−1). Then, the constitutive equations of different phase regimes (α + β and single β phases) were developed on the basis of experimental stress-strain data. The influence of the strain has been incorporated in the constitutive equation by considering its effect on different material constants for the TC17 titanium alloy. Furthermore, the predictability of the developed constitutive equation was verified by the correlation coefficient and average absolute relative error. The results indicated that the obtained constitutive equations could predict the high-temperature flow stress of a TC17 titanium alloy with good correlation and generalization.

Diffuse scattering and phason modes in the i-AlPdMn quasicrystalline phase

2005 ◽  
Vol 220 (12) ◽  
Author(s):  
Marc de Boissieu ◽  
Sonia Francoual
Keyword(s):  
Elastic Constant ◽  
Elastic Constants ◽  
Intensity Distribution ◽  
Diffuse Scattering ◽  
Hydrodynamic Theory ◽  
Quasicrystalline Phase ◽  
X Rays ◽  
X Ray ◽  
Long Wavelength ◽  
Diffusive Modes

AbstractWe review results obtained in the study of the diffuse scattering in the i-AlPdMn quasicrystal. Most of the diffuse scattering is the result of long wavelength phason modes. The shape and intensity distribution of the diffuse scattering is well reproduced using the generalised elasticity theory and two phason elastic constants. The temperature dependence of the diffuse scattering indicates a softening of the phason elastic constant as the temperature is lowered. Using coherent X-rays and photo-correlation X-ray spectroscopy, it is shown that phason modes are collective diffusive modes, in agreement with the hydrodynamic theory of long wavelength fluctuations in quasicrystals.

Elastic constants. II

1977 ◽  
Vol 357 (1690) ◽  
pp. 297-307
Keyword(s):  
Energy Density ◽  
Elastic Constant ◽  
Initial Stress ◽  
Elastic Constants ◽  
Interatomic Potential ◽  
Uniform Strain ◽  
Partial Derivatives ◽  
Constant Tensor ◽  
Derivatives Of

In the previous paper of this series we derived expressions for the initial stress and the elastic constant tensor for a crystal in terms of the partial derivatives of the energy density with uniform strain or sublattice displacement. In this paper we shall develop these equations further by considering the most general form of interatomic potential energies.

Determination of X-ray Elastic Constants in a Ti-14Al-21Nb Nb Alloy and a Ti-14Al-21Nb/SiC Metal Matrix Composite

1990 ◽  
Vol 34 ◽  
pp. 689-698 ◽  
Author(s):  
J. Jo ◽  
R. W. Hendricks ◽  
W. D. Brewer ◽  
Karen M. Brown
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Elastic Constant ◽  
Theoretical Calculation ◽  
Metal Matrix Composite ◽  
Elastic Constants ◽  
Metal Matrix ◽  
Intrinsic Value ◽  
X Ray

Residual stress values in a material are governed by the measurements of the atomic spacings in a specific crystallographic plane and the elastic constant for that plane. It has been reported that the value of the elastic constant depends on microstructure, preferred orientation, plastic deformation and morphology [1], Thus, the theoretical calculation of the elastic constant may deviate from the intrinsic value for a real alloy.

Transformation/Deformation Behavior and its Constitutive Equation for Ti-Ni-Cu Shape Memory Alloy

2008 ◽  
Vol 59 ◽  
pp. 129-134
Author(s):  
Yuji Takeda ◽  
Takaei Yamamoto ◽  
M. Uegaki ◽  
Hiroki Cho ◽  
Toshio Sakuma ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Constitutive Equation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Constitutive Equations ◽  
Deformation Behavior ◽  
Volume Fraction ◽  
Transformation Process ◽  
Reverse Transformation ◽  
Transformation Behavior

This paper describes the transformation and deformation behavior and its constitutive equation for Ti-41.7Ni-8.5Cu (at%) shape memory alloy. Plastic deformation after pre-deformation is investigated using the volume fraction of slip-deformed martensite. New kinetics and constitutive equations are proposed for the reverse transformation process. The material constants in the proposed equationa are determined from the results of tensile and heating/cooling tests of Ti-41.7Ni-8.5Cu (at%) shape memory alloy. The calculated results describe well the deformation and transformation behavior affected by pre-strain.

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.

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