1.1. Nature of Problem and Approach

Scaling is the quintessential aspect of every physical theory. If scaling is not understood, the theory itself is not understood. So it is not surprising that the question of scaling has occupied a central position in many problems of physics and engineering. Following Prandtl's (1904) development of the boundary layer theory, the study of scaling acquired during the last century a particularly prominent role in fluid mechanics.

In solid mechanics, the scaling problem of main interest is the effect of the size of structure on its strength. This problem is very old, in fact older than the mechanics of materials and structures. Its discussion started in the Renaissance. However, after an initial period of keen interest, little progress occured for two and half centuries, until in the first part of the 20-th century the statistical source of size effect became understood.

During the last quarter century, the non-statistical energetic source of size effect emerged as a focus of attention. Rapid progress has been taking place. The purpose of this treatise, ^[1] which expands an extensive recent review by Ba ant and Chen (1997), is to summarize this progress in a concise manner and to describe the current understanding of this rich, multifaceted phenomenon. A few new results are included as well. Emphasis is placed on quasibrittle materials, for which the problem of size effect is most acute and most complex. These are materials incapable of plastic yielding, failing due to fracture that is characterized...