France-U.S. workshop on strain localization and size effect due to cracking and damage

The understanding and modeling of the complete failure of structures made of brittle heterogeneous materials that exhibit distributed damage due to cracking has recently become a subject of keen interest in many countries, especially the United States and France. The importance of the subject for concrete structures, foundations, underground excavations and failure of soils, rocks, or ice, etc., as well as for the design of modern ceramics and composites, is generally accepted. The central issue is the localization of strain and energy dissipation due to strainsoftening damage and the inherent size effect on the failure loads as well as ductility of structures. To stimulate progress, an international research workshop, gathering the foremost experts from the United States and France, along with guests from other European countries and Japan, was held at E.N.S. de Cachan, France, under the joint sponsorship of French and U.S. governmental agencies. The lectures from the workshop, whose full texts appear in a separate proceedings volume, are reviewed in the present paper and the current status of knowledge is appraised from the perspective of the workshop. Considerable progress has been registered in tensile cracking and fracture, and the description of the size effect. However, further research is required on compression and shear fractures, rate effects and time-dependence, effect of microstructural characteristics and micromechanics of damage, numerical modeling of instabilities and bifurcations, and the probabilistic treatment.