Rock microstructure changes after hydrochemical reactions, which, in turn, leads to deterioration of mechanical properties. Thus, a quantification study on rock microstructural damage after chemical corrosion is necessary. Quantification of the microstructural damage of rocks after chemical corrosion was carried out in this study. We presented a proposal that included formulae for calculating the damage variable by analyzing the porosity changes of sandstone. The plastic deformation of sandstone specimens after soaking in chemical solution was observed. Plastic deformation can be divided into distinct stages over time. Results showed that the prepeak incremental deformation after chemical corrosion was partially due to the increase in plastic deformation before reaching the peak and to the deformation caused by pore compression. Plastic deformation is an indirect indicator of the degree of chemical corrosion of sandstone specimens. After chemical corrosion, the porosity of sandstone specimens changed consistently with the velocity of longitudinal wave. Therefore, the calculation formula of the damage variable can be used to calculate the porosity of sandstone specimens at different time periods. The chemical damage of sandstone specimens was highly consistent with the peak strain. Therefore, the damage variable based on porosity can be used to quantitatively describe the damage caused by chemical corrosion.

The accumulated plastic strain energy density at a dangerous point is studied to estimate the low cycle fatigue life that is composed of fatigue initiation life and fatigue crack propagation life. The modified Ramberg–Osgood constitutive relation is applied to characterize the stress–strain relationship of the strain-hardening material. The plastic strain energy density under uni-axial tension and cyclic load are derived, which are used as threshold and reference values, respectively. Then, a framework to assess the lives of fatigue initiation and fatigue crack propagation by accumulated plastic strain energy density is proposed. Finally, this method is applied to two types of aluminum alloy, LC9 and LY12 for low-cycle fatigue, and agreed well with the experiments.

In this study, the temperature field distribution and thermoelectric conversion efficiency of annular thermoelectric (TE) generators with functionally graded materials (FGMs) are investigated. The power series method is employed for solving a linear differential equation with variable coefficients to obtain temperature distribution, which has been proved to have good convergence and high precision. Numerical studies are carried out on FGM TE generators with linear and exponential variation, respectively. Material parameters that vary dependently and independently are discussed. If the figure of merit parameter Z keeps constant, then increases in the maximal conversion efficiency are not obvious. If material parameters vary independently, then the Seebeck coefficient increases from the cold temperature end to the hot temperature end and the maximal efficiency reaches 17.86%, which increases by 25.86% over 14.19% of homogeneous materials. For temperature-dependent TE materials, the problem could also be simplified to a functionally graded problem by presupposing an initial temperature field distribution. All these results give theoretical guidance for optimization of annular TE generators by using functionally graded structures.

To investigate Lamb waves in thin films made of functionally graded viscoelastic material, we deduce the governing equation with respect to the displacement component and solve these partial differential equations with complex variable coefficients based on a power series method. To solve the transcendental equations in the form of a series with complex coefficients, we propose and optimize the minimum module approximation (MMA) method. The power series solution agrees well with the exact analytical solution when the material varies along its thickness following the same exponential function. When material parameters vary with thickness with the same function, the effect of the gradient properties on the wave velocity is limited and that on the wave structure is obvious. The influence of the gradient parameter on the dispersion property and the damping coefficient are discussed. The results should provide nondestructive evaluation for viscoelastic material and the MMA method is suggested for obtaining numerical results of the asymptotic solution for attenuated waves, including waves in viscoelastic structures, piezoelectric semiconductor structures, and so on.