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Silicon, renowned for its remarkable energy density, has emerged as a focal point in the pursuit of high-energy storage solutions for the next generation. Nevertheless, silicon electrodes are known to undergo significant volume expansion during the insertion of lithium ions, leading to structural deformation and the development of internal stresses, and causing a rapid decline in battery capacity and overall lifespan. To gain deeper insights into the intricacies of charge rate effects, this study employs a combination of in situ measurements and computational modeling to elucidate the cyclic performance of composite silicon electrodes. The findings derived from the established model and curvature measurement system unveil the substantial alterations in stress and deformation as a consequence of varying charge rates. Notably, the active layer experiences compressive forces that diminish as the charge rate decreases. At a charge rate of 0.2, the active layer endures a maximum stress of 89.145 MPa, providing a comprehensive explanation for the observed deterioration in cycling performance at higher charge rates. This study not only establishes a fundamental basis for subsequent stress analyses of silicon electrodes but also lays a solid foundation for further exploration of the impact of charge rates on composite silicon electrodes. [ABSTRACT FROM AUTHOR]

The stress evolution, total charging time and capacity utilization of pulse charging (PC) method are investigated in this paper. It is found that compared to the conventional constant current (CC) charging method, the PC method can accelerate the charging process but will inevitably cause an increase in stress and a decrease in capacity. The charging speed for PC method can be estimated by the mean current. By introducing stress control, a modified PC method called the PCCC method, which starts with a PC operation followed by a CC operation, is proposed. The PCCC method not only can accelerate charging process but also can avoid the stress raising and capacity loss occurring in the PC method. Furthermore, the optimal pulsed current density and switch time in the PCCC method is also discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, structural configuration of layered Li-ion battery electrode plates is evaluated by analytically formulating the diffusion induced stress. Both symmetric electrode and asymmetric bilayer electrode are discussed. The thickness ratio and the modulus ratio of current collector to active plate are analytically identified to be the important influence parameters on the stress. Applying a material with smaller elastic modulus for current collector could reduce the peak stresses in both current collector and active plate. Increasing the thickness of current collector would reduce the stress in itself while promote the stress in active plate. Therefore, from mechanical viewpoint on designing an electrode, the material for current collector should be as soft and flexible as possible. And the thickness of current collector should be in an appropriate range. Basically, it should be as small as possible on the precondition that the mechanical strength is satisfied. Finally, effects of three charging conditions, i.e. uniform, galvanostatic, and potentiostatic, on the diffusion induced stress is discussed. It is found the maximum stresses for three cases are linear to the total amount of intercalated lithium ions. Based on the stresses, an optimized charging operation, i.e. first galvanostatic followed by potentiostatic, is suggested. [Copyright &y& Elsevier]

Abstract: This work established a new analytical model based upon the equivalent constraint model (ECM) to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading, by taking into account the effect of matrix cracking. The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate. Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates, is introduced for the construction of the failure criterion. The effects of lamina properties, lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper. A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems. The theory predictions demonstrated great match with the experimental observations investigated in this study. [Copyright &y& Elsevier]

In this article a theoretical model based upon micromechanical analysis of damage is developed to predict nonlinear stress-strain response and progressive failure of continuous fiber-reinforced metal matrix composites (MMCf). A micromechanically analytical model using an influence function superimposition technique is developed to derive stress profiles for any configuration of breaks in MMCf under tensile loading, by considering local matrix tensile yield and interface yield (or sliding). Several hundred Monte Carlo simulations including these failure mechanisms have been executed to simulate failure process and determine statistically the ultimate strength distributions of the composites. Site discretization, material sizes and shape parameter in Weibull distribution are studied to investigate the dependence of ultimate strength on these factors. It is shown that the size dependence of composite ultimate strength is dominated by fiber strength statistics and stress redistribution due to progressive microdamage. [ABSTRACT FROM AUTHOR]

Abstract: The problem of a steady line heat source within a decagonal quasicrystalline half-space, in which the boundary is traction-free, is investigated in detail by applying the complex variable technique. The line heat source is infinitely long in the period direction, then the plane strain condition prevails. The four complex stress functions are derived. It is found that the determination of the complex stress functions is independent of the thermal boundary conditions. The stress fields induced by the heat source are explicitly given based on the complex stress functions. Furthermore, we consider, both qualitatively and quantitatively, the distribution of σ11 on the boundary y=0 of the half-space to demonstrate the influence of the phonon–phason coupling constant R on the stress field. [Copyright &y& Elsevier]

This two-part contribution presents a novel and efficient method to analyze the two-dimensional (2-D) electromechanical fields of a piezoelectric layer bonded to an elastic substrate, which takes into account the fully coupled electric and mechanical behaviors. In Part I, we have obtained a system of governing integro-differential equations for the structure via a variational principle. This part presents a numerical solution algorithm of the integro-differential equations and the numerical results of some applications. A numerical algorithm for solving the system of four integro-differential equations with strongly singular kernels is developed. The convergence of the numerical algorithm is discussed. The numerical results suggest that the fully coupled electromechanical analysis is helpful for a better understanding of the performance of the piezoelectric sensor and actuator. The interfacial normal stress is much higher than the interfacial shear stress, suggesting that the interfacial normal stress causes a delamination initiation. [Copyright &y& Elsevier]

The lithium diffusion in graphite anode, which is the most widely used commercial electrode material today, affects the charge/discharge performance of lithium-ion batteries. In this study, the anisotropic strain effects on lithium diffusion in graphite anodes are systematically investigated using first-principles calculations based on density functional theory (DFT) with van der Waals corrections. It is found that the effects of external applied strains along various directions of Li x C 6 (i.e., perpendicular or parallel to the basal planes of the graphite host) on lithium diffusivity are different. Along the direction perpendicular to the graphite planes, the tensile strain facilitates in-plane Li diffusion by reducing the energy barrier, and the compressive strain hinders in-plane Li diffusion by raising the energy barrier. In contrast, the in-plane biaxial tensile strain (parallel to the graphite planes) hinders in-plane Li diffusion, and the in-plane biaxial compressive strain facilitates in-plane Li diffusion. Furthermore, both in-plane and transverse shear strains slightly influence Li diffusion in graphite anodes. A discussion is presented to explain the anisotropic strain dependence of lithium diffusion. This research provides data for the continuum modelling of the electrodes in the lithium-ion batteries. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a strategy to reduce the diffusion induced stress and enhance the capacity of a layered electrode by allowing the plastic deformation of current collector. Based on analytical formulations of the stress in whole electrode, three types of elastoplastic behaviors of current collector, i.e. pure elastic deformation, plastic shakedown and cyclic plasticity, are identified. Criterions separating the three cases are proposed. It is found applying a thin current collector and allowing it to plastically yield in the charge/discharge cycles is beneficial not only to capacity as more space can be provided for active materials but also to electrochemical stability because the stress in active layer is significantly reduced. Structural design corresponding to plastic shakedown shows good balance between the said improvements and structural safety, whereas the case of cyclic plasticity further enhances the improvements. Therefore, structural designing scheme is provided for the former case according to the criterion of plastic shakedown but for the latter one based on the Coffin–Manson relation with expected cycle life. [Copyright &y& Elsevier]

Abstract This article sheds light on advantages of fast charging methods with time-varying current. Analytical solutions of concentration and stress for charging processes with general time-varying currents are derived. A fast charging protocol for a multistage constant current of gradually decreasing value is first evaluated. A properly designed multistage constant-current method is able to simultaneously suppress stress overflow and accelerate charging, but stress undulation induced by sharp switching between stages is inevitable. A charging scheme with a nonlinear exponential current is then investigated. The applied current varies continuously and smoothly with time so stress undulation is avoided. Suggestions for the design of an exponential current method are proposed to achieve the best charging acceleration without sacrificing charging capacity or increasing risk of mechanical failures. A well-designed exponential-current method is superior to a multistage constant-current method in accelerating charging speed. [ABSTRACT FROM AUTHOR]

Mechanical properties and lithiation-induced stress are crucial to the performance and durability of lithium-ion batteries. Here, we report the evolution of elastic modulus and stress in a silicon/polyvinylidene fluoride (PVDF) composite electrode coated on a copper foil, along with a model for analyzing the large change in the radius of curvature of the composite electrode/copper foil cantilever. The radius of curvature of the cantilever is captured by a video camera during lithiation/delithiation. The elastic modulus of the composite electrode decreases from about 0.64 GPa to 0.18 GPa during lithiation. It decreases further to about 0.10 GPa after delithiation, which is caused by the fracture of the electrode. The magnitude of the compressive stress increases lineally during lithiation and decreases suddenly to reach a steady state value during delithiation. [ABSTRACT FROM AUTHOR]

Abstract: A semi-analytical method based on the cohesive model has been developed to investigate the progressive growth of interface delamination in an axisymmetric thin film electrode driven by diffusion-induced stresses under the assumption that the electrode remains elastic during the Li-ion diffusion process. The evolutions of the cohesive zone and debonding zone with respect to charging time have been predicted. The cohesive zone propagates in an accelerating manner and the debonding zone advances in a slowing down manner. The key parameters that control the interfacial stresses and delamination have been identified from the obtained governing equations. And according to the discussions on the key parameters, design insights into the geometry, charging velocity and material properties of the electrode have been provided. [Copyright &y& Elsevier]