Assessment of the local stress state through macroscopic variables

Macroscopic quantities beyond effective elastic tensors are presented that can be used to assess the local state of stress within a composite in the linear elastic regime. These are presented in a general homogenization context. It is shown that the gradient of the effective elastic property can be used to develop a lower bound on the maximum pointwise equivalent stress in the fine-scale limit. Upper bounds are more sensitive and are correlated with the distribution of states of the equivalent stress in the finescale limit. The upper bounds are given in terms of the macrostress modulation function. This function gauges the magnitude of the actual stress. For 1