| The common type of material's microscope damage is void-type damage defects, during the material processing and using, the void's aggregation and expansion would significantly reduce the material properties. The investigation of void-healing process and condition is of great value in theoretical study and engineering field, such as improve the quality of the material preparation and the manufacturing technique and the recovery of material properties that has attracted attention recently.First, in this thesis, based on a non-local elastic theory, establish the dynamic mechanical model of a void in grain under the small scale effect, then an analytical method is presented to investigate effects of the small scale parameter on the shrinkage rate of a void in grain under the hydrostatic and internal pressure in the case of two and three dimensions. From example calculations it is seen that effects of the small scale parameter on the shrinkage rate of a void in stressed grain gradually increase as the size of void shrinks smaller and smaller; the shrinkage rate changes rapidly as the hydrostatic pressure grows. The result obtained gives a reference to reveal the effects of small scale on the self-healing mechanism of the damage defects in stressed materials subjected to hydrostatic pressures.Second, based on piezoelectric theory, establish the dynamic mechanical model of a void in orthotropic materials under the piezoelectric effect, then an analytical method is presented to investigate the piezoelectric effects on the shrinkage rate of a void in piezoelectric grain under the hydrostatic, internal pressure and electric potential in the case of two and three dimensions. From example calculations it is seen that piezoelectric effect is obvious on the healing of a void as the size of void shrinks smaller and smaller; the shrinkage rate changes rapidly as the hydrostatic pressure grows; the shrinkage rate get smaller as the electric potential increases.
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