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.

A theory is developed to predict the evolution of transverse ply cracking in a composite laminate as a function of the underlying statistical fracture toughness and the applied load. Th e instantaneous formation of a matrix crack spanning both the ply thickness and the ply width is assumed to be governed by the energy criterion associated with the material fracture oughness, Γ, at the ply level. Assume multiple matrix fractures occur quasi statically and sequentially such that the ply cracks form one after another under the constant external load imposed on the specimen. Th e number of cracks, n, within the gauge length, 2L, is a discrete random variable for a given applied load, σ, because the fracture toughness varies with the location of fractures in a given specimen as well as from specimen to specimen. Th e probability function f (n, σ, L) of the discrete random variable, n, is determined from the fracture toughness distribution and the solution for the potential energy release rate. Consequently, the distribution of the crack density, dn-n/2L, is obtained. Finally, the mean crack density is formulated as a function of the applied load.