Random initial heterogeneity and degradation in brittle materials

The question of implementation of the initial state of the material is addressed. The problem is tackled by assuming random initial values for a relevant variable, within a prespecified range. The numerical implementation shows that the lower the initial assigned degradation in the material the higher the rate of dissipated energy. This numerical result agrees with relevant experiments. 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. 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.