To close on a philosophical note, consider the gradual expansion of human knowledge (Fig. 11.1). What is known may be imagined to form a circle. The unknown is what lies outside. What can be discovered at any given stage of history is only what is in contact with the circle. Questions about what lies farther into the future, not in contact with the circle, cannot even be raised.

Figure 11.1: Damage mechanics in the perspective of the expansion of human knowledge

In our field, the problem of strength of elastic frames was not even posed before Hooke. It started to be tackled in the middle of the 19th century and has been for the most part solved around 1960.

One of the most formidable problems in physics and mathematics has been that of turbulent flow. It has occupied the best minds for over a century and, as experts say, complete understanding is not yet in sight. The problem of scaling in quasibrittle materials is a part of damage mechanics, in which serious research started around 1960. Although much has been learned, it appears that damage mechanics is a formidable problem whose difficulty may be of the same dimension as turbulence. It will take a long time to resolve completely.

For the immediate future and only such a view is possible now, the following is a sample of research directions that may be identified as necessary and potentially profitable:

1. Micromechanical basis of softening damage.

2. Physically justified nonlocal model (based on the interactions...