Table of Content

01 December 2021, Volume 42 Issue 12

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Articles

Unified simulation of hardening and softening effects for metals up to failure

Siyu WANG, Lin ZHAN, Huifeng XI, O. T. BRUHNS, Heng XIAO

2021, 42(12):  1685-1702.  doi:10.1007/s10483-021-2793-6

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Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J₂-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form. With no need to identify any adjustable parameters, the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars. As such, the objectives in three respects are achieved for the first time, i.e., (i) both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors, (ii) the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed, and (iii) the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening. With the new model, the complete response features of stretched bars and twisted tubes up to failure are studied, including the failure effects of bars under monotonic extension and tubes under monotonic torsion and, furthermore, the fatigue failure effects of bars under cyclic loading. The results show accurate agreement with the uniaxial data, and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.

Prelithiation design for suppressing delamination in lithium-ion battery electrodes

Yifei QIAN, Bo LU, Yinhua BAO, Yanfei ZHAO, Yicheng SONG, Junqian ZHANG

2021, 42(12):  1703-1716.  doi:10.1007/s10483-021-2800-8

Abstract ( 1190 )   HTML ( 4)   PDF (1424KB) ( 156 )  

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Prelithiation has been intensively investigated in high-capacity lithiumion batteries (LIBs). However, the optimization of prelithiation degrees for long service life of LIBs still remains a challenge. The positive effect of prelithiation on suppressing degradation of LIBs, besides directly pursuing the high first Coulomb efficiency which has been widely reported in the literature, is revealed and discussed based on an analytical model focusing on the interfacial delamination in electrodes. For full charge-discharge cycling, well-designed prelithiation can effectively suppress the delamination and reduce the debonding size by approximately 25%, compared with the case without prelithiation. For the strategy combining partial charge-discharge cycling and prelithiation, the largest reversible capacity without debonding can be significantly improved by approximately 100% with well-designed prelithiation. This work is expected to provide a prelithiation design principle and further improve the mechanical stability of LIB electrodes.

Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube

Shitang CUI, Xiaojun NI

2021, 42(12):  1717-1732.  doi:10.1007/s10483-021-2805-6

Abstract ( 1168 )   HTML ( 4)   PDF (304KB) ( 109 )  

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An analytical model for the propagation of combined stress waves in a functionally graded thin-walled tube subjected to combined longitudinal and torsional impact loading is established. The material properties of the tube are assumed to be continuously graded along the length according to a power law function with respect to the volume fractions of the constituents. The generalized characteristic theory is used to analyze the main features of the characteristic wave speeds and simple wave solutions in the functionally graded thin-walled tube. The finite difference method is used to discretize the governing equations. Two types of typical solutions are obtained for the functionally graded tube and the homogeneous tube subjected to combined longitudinal and torsional step loading. The numerical results reveal some abnormal phenomena in the stress path and wave process of the functionally graded thin-walled tube.

Low-velocity impact of rectangular foam-filled fiber metal laminate tubes

Jianxun ZHANG, Haoyuan GUO

2021, 42(12):  1733-1742.  doi:10.1007/s10483-021-2799-7

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Through theoretical analysis and finite element simulation, the low-velocity impact of rectangular foam-filled fiber metal laminate (FML) tubes is studied in this paper. According to the rigid-plastic material approximation with modifications, simple analytical solutions are obtained for the dynamic response of rectangular foam-filled FML tubes. The numerical calculations for low-velocity impact of rectangular foam-filled FML tubes are conducted. The accuracy of analytical solutions and numerical results is verified by each other. Finally, the effects of the metal volume fraction of FMLs, the number of the metal layers in FMLs, and the foam strength on the dynamic response of foam-filled tubes are discussed through the analytical model in details. It is shown that the force increases with the increase in the metal volume fraction in FMLs, the number of the metal layers in FML, and the foam strength for the given deflection.

Power spectral density analysis for nonlinear systems based on Volterra series

Penghui WU, Yan ZHAO, Xianghong XU

2021, 42(12):  1743-1758.  doi:10.1007/s10483-021-2794-7

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A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation. A similar phenomenon also exists in random vibration. The power spectral density (PSD) analysis of random vibration for nonlinear systems is studied in this paper. The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function (GFRF). For a class of nonlinear systems, the growing exponential method is used to determine the first 3rd-order GFRFs. The proposed approach is used to achieve the nonlinear system's output PSD under a narrow-band stationary random input. The relationship between the peak of PSD and the parameters of the nonlinear system is discussed. By using the proposed method, the nonlinear characteristics of multi-band output via single-band input can be well predicted. The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system's output PSD. This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

Mengjiao HUA, Yu WU

2021, 42(12):  1759-1770.  doi:10.1007/s10483-021-2804-8

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The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits. To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation (FPE), we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation (UCNA). Subsequently, the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function (SPDF). The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect, which is in contrast to that of the uncorrelated Gaussian white noise case, where the parameter is absent from the governing equation, i.e., the most probable steady states are mainly controlled by the uncorrelated multiplicative noise. Additionally, in comparison with the deterministic counterpart, some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise, the noise intensity, and the non-Gaussian noise deviation parameter are discussed. Moreover, the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned. Furthermore, the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo (MC) simulations of the original system.

Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models

Yanli QIAO, Xiaoping WANG, Huanying XU, Haitao QI

2021, 42(12):  1771-1786.  doi:10.1007/s10483-021-2796-8

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Fractional calculus has been widely used to study the flow of viscoelastic fluids recently, and fractional differential equations have attracted a lot of attention. However, the research has shown that the fractional equation with constant order operators has certain limitations in characterizing some physical phenomena. In this paper, the viscoelastic fluid flow of generalized Maxwell fluids in an infinite straight pipe driven by a periodic pressure gradient is investigated systematically. Consider the complexity of the material structure and multi-scale effects in the viscoelastic fluid flow. The modified time fractional Maxwell models and the corresponding governing equations with distributed/variable order time fractional derivatives are proposed. Based on the L₁-approximation formula of Caputo fractional derivatives, the implicit finite difference schemes for the distributed/variable order time fractional governing equations are presented, and the numerical solutions are derived. In order to test the correctness and availability of numerical schemes, two numerical examples are established to give the exact solutions. The comparisons between the numerical solutions and the exact solutions have been made, and their high consistency indicates that the present numerical methods are effective. Then, this paper analyzes the velocity distributions of the distributed/variable order fractional Maxwell governing equations under specific conditions, and discusses the effects of the weight coefficient ϖ(α) in distributed order time fractional derivatives, the order α(r, t) in variable fractional order derivatives, the relaxation time λ, and the frequency ω of the periodic pressure gradient on the fluid flow velocity. Finally, the flow rates of the distributed/variable order fractional Maxwell governing equations are also studied.

Melting effect and Cattaneo-Christov heat flux in fourth-grade material flow through a Darcy-Forchheimer porous medium

T. HAYAT, K. MUHAMMAD, A. ALSAEDI

2021, 42(12):  1787-1798.  doi:10.1007/s10483-021-2798-6

Abstract ( 1189 )   HTML ( 1)   PDF (470KB) ( 87 )  

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The melting phenomenon in two-dimensional (2D) flow of fourth-grade material over a stretching surface is explored. The flow is created via a stretching surface. A Darcy-Forchheimer (D-F) porous medium is considered in the flow field. The heat transport is examined with the existence of the Cattaneo-Christov (C-C) heat flux. The fourth-grade material is electrically conducting subject to an applied magnetic field. The governing partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by appropriate transformations. The solutions are constructed analytically through the optimal homotopy analysis method (OHAM). The fluid velocity, temperature, and skin friction are examined under the effects of various involved parameters. The fluid velocity increases with higher material parameters and velocity ratio parameter while decreases with higher magnetic parameter, porosity parameter, and Forchheimer number. The fluid temperature is reduced with higher melting parameter while boosts against higher Prandtl number, magnetic parameter, and thermal relaxation parameter. Furthermore, the skin friction coefficient decreases against higher melting and velocity ratio parameters while increases against higher material parameters, thermal relaxation parameter, and Forchheimer number.

Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control

Xuhui WANG, Nanjing HUANG

2021, 42(12):  1799-1816.  doi:10.1007/s10483-021-2789-6

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The leaderless and leader-following finite-time consensus problems for multiagent systems (MASs) described by first-order linear hyperbolic partial differential equations (PDEs) are studied. The Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic PDEs. Finally, two numerical examples are provided to verify the effectiveness of the proposed methods.