Effects of growth on the deformation and the stability of hyper-elastic spherical shells

A mechanical model for the large deformation analysisof an incompressible hyper-elastic spherical shell subjected to theinner pressure is established within the framework of the finite elasticitytheory of continuum mechanics. The effect of growth on the deformation andthe stability of the shell are examined with the elastic model forvolumetric growth based on multiplicative decomposition of the deformationgradient. The deformation curves and the distribution of stresses, theresidual strain and the distribution of residual stresses due to growth aregiven by numerical computation of the relation between the deformation andthe inner pressure. It is shown that the effect of growth on the deformationof the shell is obvious. The critical thickness and the critical pressurefor the shell to take an unstable deformation are affected by growth, andthe stability of the shell may be changed by growth in some cases. Residualdeformation 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 bya sufficiently large growth even in the absence of the external loading.