[en] A fully coupling model for the diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries is proposed. The effect of the mechanical stress on the lithium diffusion is accounted for by the mechanical part of the chemical potential derived from the Gibbs free energy along with the logarithmic stress and strain. Eight dimensionless parameters, governing the stress-assisted diffusion and the diffusion induced elastoplastic bending, are identified. It is found that the finite plasticity starting from the interface of the bilayer increases the chemical potential gradient and thereby facilitates the lithium diffusion. The full plastic flow makes the abnormal lithium concentration distribution possible, i.e., the concentration at the lithium inlet can be lower than the concentration at the interface (downstream). The increase in the thickness of the active layer during charging is much larger than the eigen-stretch due to lithiation, and this excess thickening is found to be caused by the lithiation induced plastic yield.

[en] Intercalation of lithium ions into the electrodes of lithium ion batteries is affected by the stress of active materials, leading to energy dissipation and stress dependent voltage hysteresis. A reaction-diffusion-stress coupling model is established to investigate the stress effects under galvanostatic and potentiostatic operations. It is found from simulations that the stress hysteresis contributes to the voltage hysteresis and leads to the energy dissipation. In addition, the stress induced voltage hysteresis is small in low rate galvanostatic operations but extraordinarily significant in high rate cases. In potentiostatic operations, the stresses and stress induced overpotentials increase to a peak value very soon after the operation commences and decays all the left time. Therefore, a combined charge-discharge operation is suggested, i.e., first the galvanostatic one and then the potentiostatic one. This combined operation can not only avoid the extreme stress during operations so as to prevent electrodes from failure but also reduce the voltage hysteresis and energy dissipation due to stress effects.

[en] The time-dependent electro-viscoelastic performance of a circular dielectric elastomer (DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.

[en] The nonlocal peridynamic theory has been proven to be a promising method for the material failure and damage analyses in solid mechanics. Based upon the integrodifferential equations, peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving, and arrest. In this paper, the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch, which is widely used to investigate the mixed I-II crack propagation in brittle materials. The predictions from the peridynamic analysis agree well with available experimental observations. The numerical results show that the dynamic fracture behaviors of the beam under the impact load, such as crack initiation, curving, and branching, rely on the location of the offset notch and the impact speed of the drop hammer.

[en] This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solution procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geometric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young’s modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.

[en] The initial value problem for the quantum Zakharov equation in three dimensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

[en] Linear and weakly nonlinear analyses are made for the Rayleigh-B´enard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret co-efficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in-fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap-pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.

[en] Turbulent gas-particle flows are studied by a kinetic description using a probability density function (PDF). Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are directly solved either using a finite-difference method for two-dimensional (2D) problems or using a Monte-Carlo (MC) method for three-dimensional (3D) problems. The proposed differential stress model together with the PDF (DSM-PDF) is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment (SOM) two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

[en] A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the problem is established. With the multiplier method, a uniform decay result is proven.

[en] Rayleigh-Taylor (R-T) instability is known as the fundamental mechanism of equatorial plasma bubbles (EPBs). However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows: if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments are designed to validate the sufficient conditions. The results agree with the derived sufficient conditions.