Through dimension analysis, an almost analytical model for the maximum diffusion induced stress (DIS) and critical temperature (or concentration) difference at which cracks begin to initiate in the diffusion process is developed. It interestingly predicts that the spacing of diffusioninduced cracks is constant, independent of the thickness of specimen and the temperature difference. These conclusions are validated by our thermal shock experiments on alumina plates. Furthermore, the proposed model can interpret observed hierarchical crack patterns for high temperature jump cases, and a three-stage relation between the residual strength and the temperature difference. The prediction for crack spacing can guide the biomimetic thermal-shockfailure proof design, in which the hard platelets smaller than the predicted diffusion induced by constant crack-spacing are embedded in a soft matrix, and, therefore, no fracture will happen. This may guide the design of the thermal protection system and the lithium ion battery. Finally we present the maximum normalized DISes for various geometry and boundary conditions by single-variable curves for the stressindependent diffusion process and two-variable contour plots engineers and materialists a simple and easy way to quickly evaluate the reliability of related materials and devices.

This paper investigates what is the largest magnetoelectric (ME) coefficient of ME composites, and how to realize it. From the standpoint of energy conservation, a theoretical analysis is carried out on an imaginary lever structure consisting of a magnetostrictive phase, a piezoelectric phase, and a rigid lever. This structure is a generalization of various composite layouts for optimization on ME effect. The predicted theoretical ultimate ME coefficient plays a similar role as the efficiency of ideal heat engine in thermodynamics, and is used to evaluate the existing typical ME layouts, such as the parallel sandwiched layout and the serial layout. These two typical layouts exhibit ME coefficient much lower than the theoretical largest values, because in the general analysis the stress amplification ratio and the volume ratio can be optimized independently and freely, but in typical layouts they are dependent or fixed. To overcome this shortcoming and achieve the theoretical largest ME coefficient, a new design is presented. In addition, it is found that the most commonly used electric field ME coefficient can be designed to be infinitely large. We doubt the validity of this coefficient as a reasonable ME effect index and consider three more ME coefficients, namely the electric charge ME coefficient, the voltage ME coefficient, and the static electric energy ME coefficient. We note that the theoretical ultimate value of the static electric energy ME coefficient is finite and might be a more proper measure of ME effect.