On shakedown analysis in hardening plasticity

The extension of classical shakedown theorems for hardening plasticity is interesting from both theoretical and practical aspects of the theory of plasticity. This problem has been much discussed in the literature. In particular, the model of generalized standard materials gives a convenient framework to derive appropriate results for common models of plasticity with strain-hardening. This paper gives a comprehensive presentation of the subject, in particular, on general results which can be obtained in this framework. The extension of the static shakedown theorem to hardening plasticity is presented at first. It leads by min-max duality to the definition of dual static and kinematic safety coefficients in hardening plasticity. Dual static and kinematic approaches are discussed for common models of isotropic hardening of limited or unlimited kinematic hardening. The kinematic approach also suggests for these models the introduction of a relaxed kinematic coefficient following a method due to Koiter. Some models for soils such as the Cam-clay model are discussed in the same spirit for applications in geomechanics. In particular, new appropriate results concerning the variational expressions of the dual kinematic coefficients are obtained.     

Two-way coupled analysis of lithium diffusion and diffusion induced finite elastoplastic bending of bilayer electrodes in lithium-ion batteries

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.     

Pressure-sensitive plasticity of lithiated silicon in Li-ion batteries

Lithiation-induced plasticity is a key factor that enables Si electrodes to maintain long cycle life in Li-ion batteries. We study the plasticity of various lithiated sili-con phases based on first-principles calculations and iden-tify the linear dependence of the equivalent yield stress on the hydrostatic pressure. Such dependence may cause the compression-tension asymmetry in an amorphous Si thin film electrode from a lithiation to delithiation cycle, and leads to subsequent ratcheting of the electrode after cyclic lithiation. We propose a yield criterion of amorphous lithi-ated silicon that includes the effects of the hydrostatic stress and the lithiation reaction. We further examine the micro-scopic mechanism of deformation in lithiated silicon under mechanical load, which is attributed to the flow-defects mediated local bond switching and cavitation. Hydrostatic compression confines the flow defects thus effectively strength-ens the amorphous structure, and vice versa.     

Prelithiation design for suppressing delamination in lithium-ion battery electrodes

Applied Mathematics and Mechanics - Prelithiation has been intensively investigated in high-capacity lithium-ion batteries (LIBs). However, the optimization of prelithiation degrees for long...     

Strong dependency of lithium diffusion on mechanical constraints in high-capacity Li-ion battery electrodes

The effect of external constraints on Li diffusion in high-capacity Li-ion battery electrodes is investigated us- ing a coupled finite deformation theory. It is found that thin- film electrodes on rigid substrates experience much slower diffusion rates compared with free-standing films with the same material properties and geometric dimensions. More importantly, the study reveals that mechanical driving forces tend to retard diffusion in highly-constrained thin films when lithiation-induced softening is considered, in contrast to the fact that mechanical driving forces always enhance diffusion when deformation is fully elastic. The results provide further proof that nano-particles are a better design option for next-generation alloy-based electrodes compared with thin films.     

Research progress in degradation mechanism of silicon anode materials for lithium-ion batteries

硅负极材料由于具有非常高的理论比容量,使之成为锂离子电池极具前景的负极替代材料,然而,硅负极材料在充放电过程中会发生非常大的体积变形,这会引起活性材料的破坏失效,严重影响其电化学循环性能,成为制约其在锂离子电池领域广泛应用的最大瓶颈,本文介绍了硅负极材料的不同结构形态及其在充放电过程中电化学性能的退化机理,并综述了充放电过程中的力学性能演化、相关理论分析、数值模拟计算等方面的最新国际研究进展,展望了硅负极材料力学失效方面的研究重点,     

Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes

Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.     

A pre-strain strategy of current collectors for suppressing electrode debonding in lithium-ion batteries

The interfacial debonding between the active layer and the current collector has been recognized as a critical mechanism for battery fading, and thus has attracted great efforts focused on the related analyses. However, much still remains to be studied regarding practical methods for suppressing electrode debonding, especially from the perspective of mechanics. In this paper, a pre-strain strategy of current collectors to alleviate electrode debonding is proposed. An analytical model for a symme...     

Electrochemical performance of polygonized carbon nanofibers as anode materials for lithium-ion batteries

Carbon nanofibers with a polygonal cross section (P-CNFs) synthesized using a catalytic chemical vapor deposition (CCVD) technology have been investigated for potential applications in lithium batteries as anode materials. P-CNFs exhibit excellent high-rate capabilities. At a current density as high as 3.7 and 7.4 A/g, P-CNFs can still deliver a reversible capacity of 198.4 and 158.2 mAh/g, respectively. To improve their first coulombic efficiency, carbon-coated P-CNFs were prepared through thermal vapor deposition (TVD) of benzene at 900 °C. The electrochemical results demonstrate that appropriate amount of carbon coating can improve the first coulombic efficiency, the cycling stability and the rate performance of P-CNFs. After carbon coating, P-CNFs gain a weight increase approximately by 103 wt%, with its first coulombic efficiency increasing from 63.1 to 78.4%, and deliver a reversible capacity of 197.4 mAh/g at a current density of 3.7 A/g. After dozens of cycles, there is no significant capacity degradation at both low and high current densities.     

Mesoporous composite of LiFePO4 and carbon microspheres as positive-electrode materials for lithium-ion batteries

Mesoporous LiFePO4/C microspheres consisting of LiFePO4 nanoparticles are successfully fabricated by an eco-friendly hydrothermal approach combined with high-temperature calcinations using cost-effective LiOH and Fe3＋ salts as raw materials.In this strategy,pure mesoporous LiFePO4 microspheres,which are composed of LiFePO4 nanoparticles,were uniformly coated with carbon（1.5nm）.Benefiting from this unique architecture,these mesoporous LiFePO4/C microspheres can be closely packed,having high tap density.The initial discharge capacity of LiFePO4/C microspheres as positive-electrode materials for lithium-ion batteries could reach 165.3 mAh/g at 0.1 C rate,which is notably close to the theoretical capacity of LiFePO4 due to the large BET surface area,which provides for a large electrochemically available surface for the active material and electrolyte.The material also exhibits high rate capability（100 mAh/g at 8 C） and good cycling stability（capacity retention of 92.2%after 400 cycles at 8 C rate）.     

Mesoporous composite of LiFePO4 and carbon microspheres as positive-electrode materials for lithium-ion batteries

Mesoporous LiFePO₄/C microspheres consisting of LiFePO₄ nanoparticles are successfully fabricated by an eco-friendly hydrothermal approach combined with high-temperature calcinations using cost-effective LiOH and Fe³⁺ salts as raw materials. In this strategy, pure mesoporous LiFePO₄ microspheres, which are composed of LiFePO₄ nanoparticles, were uniformly coated with carbon (∼1.5 nm). Benefiting from this unique architecture, these mesoporous LiFePO₄/C microspheres can be closely packed, having high tap density. The initial discharge capacity of LiFePO₄/C microspheres as positive-electrode materials for lithium-ion batteries could reach 165.3 mAh/g at 0.1 C rate, which is notably close to the theoretical capacity of LiFePO₄ due to the large BET surface area, which provides for a large electrochemically available surface for the active material and electrolyte. The material also exhibits high rate capability (∼100 mAh/g at 8 C) and good cycling stability (capacity retention of 92.2% after 400 cycles at 8 C rate).     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

Integrating trace Ti-doping and LiYO2-coating to stabilize Ni-rich cathodes for lithium-ion batteries

Ni-rich layered cathodes have become the promising candidates for the next-generation high-energy Li-ion batteries due to their high energy density and competitive cost. However, they suffer from rapid capacity fading due to the structural and interfacial instability upon long-term operation. Herein, the Ti-doped and LiYO₂-coated Ni-rich layered cathode has been synthesized via a facile one-step sintering strategy, which significantly restrains the interfacial parasitic side reactions and enhances the structural stability. Specifically, the trace Ti⁴⁺ doping greatly stabilizes the lattice oxygen and alleviates the Li/Ni disorder while the LiYO₂ coating layer can prevent the erosion of the cathode by the electrolyte during cycles. As a result, the Ti-NCM83@LYO delivers a high specific capacity of 135 mAh g⁻¹ even at 10C and there is almost no capacity loss at 1C for 100 cycles. This work provides a simple one-step dual-modification strategy to meet the commercial requirements of Ni-rich cathodes.     

Microwave-assisted polyol synthesis of LiMnPO4/C and its use as a cathode material in lithium-ion batteries

We synthesized LiMnPO₄/C with an ordered olivine structure by using a microwave-assisted polyol process in 2:15 (v/v) water–diethylene glycol mixed solvents at 130 °C for 30 min. We also studied how three surfactants—hexadecyltrimethylammonium bromide, polyvinylpyrrolidone k30 (PVPk30), and polyvinylpyrrolidone k90 (PVPk90)—affected the structure, morphology, and performance of the prepared samples, characterizing them by using X-ray diffraction, scanning electron microscopy, transmission electron microscopy, charge/discharge tests, and electrochemical impedance spectroscopy. All the samples prepared with or without surfactant had orthorhombic structures with the Pnmb space group. Surfactant molecules may have acted as crystal-face inhibitors to adjust the oriented growth, morphology, and particle size of LiMnPO₄. The microwave effects could accelerate the reaction and nucleation rates of LiMnPO₄ at a lower reaction temperature. The LiMnPO₄/C sample prepared with PVPk30 exhibited a flaky structure coated with a carbon layer (∼2 nm thick), and it delivered a discharge capacity of 126 mAh/g with a capacity retention ratio of ∼99.9% after 50 cycles at 1C. Even at 5C, this sample still had a high discharge capacity of 110 mAh/g, demonstrating good rate performance and cycle performance. The improved performance of LiMnPO₄ likely came from its nanoflake structure and the thin carbon layer coating its LiMnPO₄ particles. Compared with the conventional polyol method, the microwave-assisted polyol method had a much lower reaction time.     

Thermal stresses and shakedown in wheel/rail contact

Summary  Sliding friction between railway wheels and rails results in considerable contact temperatures and gives rise to severe thermal stresses at the surfaces of the wheels and rails. An approximate analytical solution is presented for a line contact model. The increased bulk temperature of the wheel after a long period of constant operating conditions is also taken into account. The thermal stresses have to be superimposed on the mechanical contact stresses. They reduce the elastic limit of the wheel and rail, and yielding begins at lower mechanical loads. When residual stresses build up during the initial cycles of plastic deformation, the structure can carry higher loads with a purely elastic response in subsequent load cycles. This phenomenon is referred to as shakedown. Due to the distribution of temperature, the rail surface is generally subjected to higher stresses than the wheel surface. This can cause structural changes in the rail material and hence rail damage. Received 7 May 2002; accepted for publication 3 September 2002     

Damage and shakedown analysis of structures with strain-hardening

In this article, the ductile damage of materials is introduced into the shakedown theory of strain-hardening structures. A mathematical programming method is developed to calculate an upper bound of the damage factor in a structure subjected to varying loads, which is suggested as the criterion of structural failure. Based on it, a lower bound of the safe load factor can be obtained for a strain-hardening structure via a mathematical programming. The application of this theory is demonstrated by analysing the thick-walled cylindrical tube.     

Limit and shakedown analysis of pressurized pipelines containing defects

In this paper, the integrity assessment of pressurized pipelines containing defects is performed by direct simplified methods of limit and shakedown analysis. The defects considered are part-through slots of various geometrical configurations. The engineering situation considered here has practical importance in the pressure vessel and pipe industry. The results are compared with those obtained by a step-by-step procedure using the professional code ABAQUS and where possible, with those provided by semi-empirical formulae used in engineering. The simplified methods are found more economical and more reliable than marching solutions achieved by step-by-step evolutive elastic-plastic analysis. The effects of various part-through slots on the load-carrying capacities of pipelines are investigated. The project was supported by the National Science and Technology Commission of China and by the Department of Structural Engineering, Technical University of Milan, Italy     

Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity

A fully nonlinear shakedown analysis is considered for structures undergoing large elastic-plastic strains. The underlying kinematics of finite elastoplasticity are based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. It is Shown that the notion of a fictitious, self-equilibrated residual stress field of Melan's linear shakesdown theorem has to be replaced by the notion of real, self-equilibrated residual state. Path-dependent and path-independent shakedown theorems are presented that can be realized in an incremental step-by-step procedure using Finite Element codes. The numerical implementation is considered for highly nonlinear truss structures undergoing large cyclic deformations with ideal-plastic, isotropic and kinematic hardening material behavior. Path-dependency of the residual states in the case of non-adaptation and path-independency in the case of shakedown are shown, and the shakedown domain is determined taking into account also the stability boundaries of the structure.     

Stress function method in shakedown analysis of axisymmetric shells

A self-equilibrated stress obtained from the stress functions of thin shells is used for the static shakedown theorem as a residual stress. In combination with the finite element method, a linear programming formulation of the shakedown analysis of axisymmetric shells is derived. The physical meaning of the stress function method is clear and its computing amount is small. Some examples of the plates and shells show that the method is reasonable and efficient.The project was supported by the National Natural Science Foundation of China