生长对超弹性球壳变形和稳定性的影响

EFFECTS OF GROWTH ON THE DEFORMATION AND THE STABILITY OF HYPER-ELASTIC SPHERICAL SHELLS

应用连续介质力学有限变形理论建立受内压作用不可压超弹性球壳大变形问题的力学模型,且运用基于变形梯度张量极分解的弹性体积生长理论分析生长对不可压超弹性球壳变形和稳定性的影响.通过对球壳变形与内压关系式的数值计算得到不同生长条件下球壳的变形曲线和应力分布曲线及由生长引起的残余变形和残余应力分布.计算结果表明生长对球壳变形特性有明显的影响,生长影响球壳可产生不稳定变形的临界壁厚和临界内压,且在某些情况下可改变球壳的稳定性.生长在球壳中可产生一定的残余变形和残余应力,对球壳中的应力分布有一定的影响.另外当生长的程度足够大时,即便没有外力作用,球壳仅在生长引起的残余应力作用下也可产生不稳定变形.

A mechanical model for the large deformation analysis of an incompressible hyper-elastic spherical shell subjected to the inner pressure is established within the framework of the finite elasticity theory of continuum mechanics. The effect of growth on the deformation and the stability of the shell are examined with the elastic model for volumetric growth based on multiplicative decomposition of the deformation gradient. The deformation curves and the distribution of stresses, the residual strain and the distribution of residual stresses due to growth are given by numerical computation of the relation between the deformation and the inner pressure. It is shown that the effect of growth on the deformation of the shell is obvious. The critical thickness and the critical pressure for the shell to take an unstable deformation are affected by growth, and the stability of the shell may be changed by growth in some cases. Residual deformation and residual stresses can be developed in the shell by growth, and the distribution of stresses also affected by growth. Furthermore, unstable deformation may be rendered only by the residual stress induced by a sufficiently large growth even in the absence of the external loading.