Assessment of iterated variational homogenization for microstructure evolution in porous materials

The purpose of this work is to assess iterated variational homogenization estimates of the evolution of relative lengths and axes of ellipsoidal pores under unhomogeneous yielding. The latter is generally understood as the percolation of elastically unloaded zones in a porous material. To this end, the instantaneous average strain rate and rotation rate of the pores are calculated by requiring the overall strain rate to be congruent with unhomogeneous yielding. The predictions are then compared against numerically determined strain and rotation rates of the pores using finite element based limit-analysis. The assessment considers the two fundamental modes of unhomogeneous yielding: opening/closure and sliding. Whether the predictions capture the extreme shearing of pores under sliding or the lateral bulging of pores under opening is discussed. For the opening mode, iterated variational homogenization performs well in predicting lateral bulging, except for nearly spherical pores. For sliding shear, the iterated variational homogenization estimates are qualitatively inaccurate and consistently underpredict the shearing and rotation rates of the pores. It is shown that simpler estimates from linear variational homogenization, augmented with ‘complementary’ concentration tensors, compare favorably with numerical results.