Heterogeneity, microstructural surface effects and internal length estimation

Recently, the concept of state of degradation has been employed by the author in order to study the effect of initial material (structure) inhomogeneity and the implications of surface (skin) effects on brittle material response. The analysis has revealed the importance of the internal material length, e.g. for assigning the initial random variables according to a material dependent fluctuation scale. Different possibilities for its estimation and/or evolution have been suggested. Here, symbolic computations by computer that resulted in the analytical solution of an instability problem are presented. Such analytical solution without computer had not been obtained in the past because the analytical work is tedious and error prone making it very difficult to pursue. The analytical solution, made possible through symbolic computations, provides significant insight into the problem of skin effects in brittle materials and internal length estimation. This paper summarizes the previous work of the author and co-workers, presents the results of symbolic computations of an instability problem, and interprets the results with respect to material length estimation.