Position and size effects on voids growth in nonlinear elasticity

Numerical studies of multiple voids growth are carried out on a nonlinear hyper-elastic 2D cylinder subjected to an expansionary boundary condition. For certain compressible hyper-elastic material, our numerical experiments on the case of two voids revealed that both the positions and initial sizes of the pre-existing voids can have significant effects on the final grown configuration. We found that, for the initial voids of macroscopic scale both factors affect the final result in a continuous manner and two grown voids of comparable size are commonly observed, and for the initial voids of mesoscopic scale the size effect is no longer continuous and one of the grown voids is always found significantly greater than the other, while for the initial voids of microscopic scale the position effect is essentially decisive on the voids growth and the center positioned void always grows much more rapidly. We also found that the size and position effects are stronger if the material is less compressible, or the load, with the smaller principle stress in alignment with the two voids, is less symmetric.