On the Constitutive Equation of Elastic Anisotropy of Shales

Author(s):  
L. Duranti
2017 ◽  
Vol 13 (2) ◽  
pp. 4705-4717
Author(s):  
Zhang Qian ◽  
Zhou Xuan ◽  
Zhang Zhidong

Basing on Landau–de Gennes theory, this study investigated the chiral configurations of nematic liquid crystals confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls. When the elastic anisotropy (L2/L1) is large enough, a new structure results from the convergence of two opposite escape directions of the heterochiral twist and escape radial (TER) configurations. The new defect presents when L2/L1≥7 and disappears when L2/L1<7. The new structure possesses a heterochiral hyperbolic defect at the center and two homochiral radial defects on both sides. The two radial defects show different chiralities.


Author(s):  
Tainan Gabardo ◽  
Cezar Otaviano Ribeiro Negrao

Author(s):  
David J. Steigmann

This chapter develops the general constitutive equation for transversely isotropic, fiber-reinforced materials. Applications include composite materials and bio-elasticity.


2020 ◽  
Vol 23 (6) ◽  
pp. 1570-1604
Author(s):  
Teodor Atanacković ◽  
Stevan Pilipović ◽  
Dora Seleši

Abstract Equations of motion for a Zener model describing a viscoelastic rod are investigated and conditions ensuring the existence, uniqueness and regularity properties of solutions are obtained. Restrictions on the coefficients in the constitutive equation are determined by a weak form of the dissipation inequality. Various stochastic processes related to the Karhunen-Loéve expansion theorem are presented as a model for random perturbances. Results show that displacement disturbances propagate with an infinite speed. Some corrections of already published results for a non-stochastic model are also provided.


Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2456
Author(s):  
Zhijun Yang ◽  
Weixin Yu ◽  
Shaoting Lang ◽  
Junyi Wei ◽  
Guanglong Wang ◽  
...  

The hot deformation behaviors of a new Ti-6Al-2Nb-2Zr-0.4B titanium alloy in the strain rate range 0.01–10.0 s−1 and temperature range 850–1060 °C were evaluated using hot compressing testing on a Gleeble-3800 simulator at 60% of deformation degree. The flow stress characteristics of the alloy were analyzed according to the true stress–strain curve. The constitutive equation was established to describe the change of deformation temperature and flow stress with strain rate. The thermal deformation activation energy Q was equal to 551.7 kJ/mol. The constitutive equation was ε ˙=e54.41[sinh (0.01σ)]2.35exp(−551.7/RT). On the basis of the dynamic material model and the instability criterion, the processing maps were established at the strain of 0.5. The experimental results revealed that in the (α + β) region deformation, the power dissipation rate reached 53% in the range of 0.01–0.05 s−1 and temperature range of 920–980 °C, and the deformation mechanism was dynamic recovery. In the β region deformation, the power dissipation rate reached 48% in the range of 0.01–0.1 s−1 and temperature range of 1010–1040 °C, and the deformation mechanism involved dynamic recovery and dynamic recrystallization.


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