The composition-gradient electrode material is considered as one of the most promising materials for lithium-ion batteries because of its excellent electrochemical performance and thermal stability. In this work, the effects of concentration-dependent elastic modulus on Li-ions diffusion and diffusion-induce stress in the composition-gradient electrodes were studied. The coupling equations of elasticity and diffusion under both potentiostatic charging and galvanostatic charging were developed to obtain the distributions of both the Li-ions concentration and the stress. The results indicated that the effects of the concentration-dependent elastic modulus on the Li-ions diffusion and the diffusion-induce stresses are controlled by the lithiation induced stiffening factor in the composition-gradient electrodes: a low stiffening factor at the center and a high stiffening factor at the surface lead to a significant effect, whereas a high stiffening factor at the center and a low stiffening factor at the surface result in a minimal effect. The results in this work provide guidance for the selection of electrode materials.

Composition-gradient electrode materials have been proven to be one of the most promising materials in lithium-ion battery. To study the mechanism of mechanical degradation in spherical composition-gradient electrodes, the finite deformation theory and reversible chemical theory are adopted. In homogeneous electrodes, reversible electrochemical reaction may increase the magnitudes of stresses. However, reversible electrochemical reaction has different influences on stresses in composition-gradient electrodes, resulting from three main inhomogeneous factors—forward reaction rate, backward reaction rate, and reaction partial molar volume. The decreasing transition form of forward reaction rate, increasing transition form of backward reaction rate, and increasing transition form of reaction partial molar volume can reduce the magnitudes of stresses. As a result, capacity fading and mechanical degradation are reduced by taking advantage of the effects of inhomogeneous factors.

In order to realize the low temperature and rapid cold start-up of a proton exchange membrane fuel cell stack, a dynamic model containing 40 single proton exchange membrane fuel cells is established to estimate the melting time of the proton exchange membrane fuel cell stack as well as to analyze the melting process of the ice by using the obtained liquid–solid boundary. The methods of proton exchange membrane electric heating and electrothermal film heating are utilized to achieve cold start-up of the proton exchange membrane fuel cell (PEMFC). The fluid simulation software fluent is used to simulate and analyze the process of melting ice. The solidification and melting model and multi-phase flow model are introduced. The pressure-implicit with splitting of operators algorithm is also adopted. The results show that both the proton exchange membrane electric heating technology and the electrothermal film heating method can achieve rapid cold start-up. The interior ice of the proton exchange membrane fuel cell stack melts first, while the first and 40th pieces melt afterwards. The ice melting time of the proton exchange membrane fuel cell stack is 32.5 s and 36.5 s with the two methods, respectively. In the end, the effect of different electrothermal film structures on cold start-up performance is studied, and three types of pore diameter electrothermal films are established. It is found that the electrothermal film with small holes melts completely first, and the electrothermal film with large holes melts completely last.