As parameters in Chaboche model are difficult to be determined from experimental data, a single objective particle swarm optimization procedure was employed to obtain them. Hysteresis loop and uniaxial and biaxial ratcheting simulations were conducted to validate the determined models. Chaboche models determined by particle swarm optimization give more accurate simulation of ratcheting compared with the model determined by trial and error method. Chaboche models containing different backstress components were studied. Models determined considering uniaxial ratcheting can only predict uniaxial ratcheting precisely, while giving very bad simulation of biaxial ratcheting. The linear hardening rule in the N3L1 model clearly decreases the rate of the accumulation of ratcheting strain, and the N3L1 model gives the best simulations. For biaxial ratcheting, the fourth backstress component can decrease the rate of the accumulation apparently, while it has a little influence on prediction of uniaxial ratcheting.

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<abstract><p>In this paper, we establish a regularity criterion for the 3D nematic liquid crystal flows. More precisely, we prove that the local smooth solution $ (u, d) $ is regular provided that velocity component $ u_{3} $, vorticity component $ \omega_{3} $ and the horizontal derivative components of the orientation field $ \nabla_{h}d $ satisfy</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} \int_{0}^{T}|| u_{3}||_{L^{p}}^{\frac{2p}{p-3}}+||\omega_{3}||_{L^{q}}^{\frac{2q}{2q-3}}+||\nabla_{h} d||_{L^{a}}^{\frac{2a}{a-3}} \mbox{d} t&lt;\infty,\nonumber \\ with\ \ 3&lt; p\leq\infty,\ \frac{3}{2}&lt; q\leq\infty,\ 3&lt; a\leq\infty. \end{eqnarray*} $\end{document} </tex-math></disp-formula></p> </abstract>

In this paper, we study the regularity criterion for the local smooth solution of the 3D nematic liquid crystal flows. More precisely, it is proved the smooth solution u , d can be extended beyond T provided that ∫ 0 T ∇ h u h B ˙ ∞ , ∞ 0 + ∇ d B ˙ ∞ , ∞ 0 2 / 1 + log 1 + ∇ u B ˙ ∞ , ∞ 0 + ∇ d B ˙ ∞ , ∞ 0 d t < ∞ or ∫ 0 T ∇ h u h B ˙ ∞ , ∞ − r 4 / 3 − 2 r + ∇ d B ˙ ∞ , ∞ 0 2 / 1 + log 1 + ∇ u B ˙ ∞ , ∞ 0 + ∇ d B ˙ ∞ , ∞ 0 d t < ∞ , 0 ≤ r ≤ 1 .

In this paper, we derive two regularity criteria of solutions to the nematic liquid crystal flows. More precisely, we prove that the local smooth solution false(u,dfalse)$$ \left(u,d\right) $$ is regular if and only if one of the following two conditions is satisfied: (i) ∇huh∈L2p2p−3false(0,T;Lpfalse(ℝ3false)false),0.1em∂3d∈L2qq−3false(0,T;Lqfalse(ℝ3false)false),0.1em32