Many artificial materials such as concrete, but also others, are characterized by larger size inclusions (the aggregate) embedded in a finer grained matrix. The embedment may be complete, i.e. surrounding the larger grains, or the finer matrix may only fill the interstices between larger inclusions which are in contact with each other. Similar conditions exist in many natural rocks and frozen sands. Evidence indicates that inclusions can both strengthen and weaken a material, i.e. the finer grained material gaining strength as inclusions are added or vice versa. The effect of inclusions can be experimentally investigated and analytically predicted through either a micro-continuum or a discontinuum approach: In the micro-continuum approach, grains are considered as rigid inclusions in a deformable matrix. The opposite, i.e. softer inclusions are also possible but this will not be dealt with in this research. By application of a homogenization scheme, the effects of the crack density on the elastic properties, and eventually on the failure load of the composite can be taken into account. However, since this involves volume averaging, which smears out the stress intensity around cracks, the continuum approach cannot capture crack propagation and coalescence, leading to a crack network. In the discontinuum approach, one specifically considers the behavior of cracks. As cracks propagate, they coalesce and eventually form thoroughgoing failure surfaces. Conversely, propagating cracks will encounter the larger grains and further propagation might be stopped.

To benefit from the relative advantages and to eliminate the disadvantages of both approaches, they will be combined to develop a predictive model which is both accurate and computationally effective. The advantages of such combination are that the micro-continuum approach is able to capture the characteristic properties of the uncracked matrix with rigid inclusions; such properties can then be used in the discontinuum approach.

The research will consist of experimental and theoretical work. Experiments will be conducted on material containing inclusions and preformed cracks to study the associated discontinuum behavior. Other experiments using nano-indentation will be conducted simultaneously to obtain information which can be used to constrain the crack propagation criterion. The theoretical work will use the experimental results to produce the combined micromechanics-discontinuum approach which, in turn, will be validated through comparison with experiments.

This research will have scientific, practical engineering and educational impacts. The scientific benefits and impacts of this work are a better fundamental understanding of material behavior. Specifically, the research will improve our understanding of the effects of inclusions and of crack propagation and coalescence, which are of utmost significance in many natural and artificial materials. -

The impact of this work on the practicing profession relates to the question as to when to apply continuum approaches and when discontinuum approaches and to define the boundary between the two. This question is as old as rational analysis and design of structures and materials. This research, while not implying to reach a final solution to this scale dependent problem, will provide mechanically based analytical tools to select the appropriate approach. As a matter of fact, it will go a step further and produce a combined continuum-discontinuum approach. Obvious materials/structures where this will have important implications in practice are rocks and many soils as well as concrete - Education will benefit from the fact that the research will be conducted by two graduate (doctoral) students and, as usual, will also include undergraduate students. The students will not only be strongly involved in the research work but also in writing papers and making oral presentations.

Project Report

Cracks and fractures play an important role in many natural and artificial materials. For instance, fractures (also called joints) on the meter to decameter scale in rock masses govern the stability and deformability of slopes and tunnels and provide avenues for water flow. Cracks in artificial materials such as concrete, for instance, on the millimeter to centimeter scale also govern the strength, deformability and permeability of the materials. What is important to know in all this is how cracks nucleate, propagate and eventually coalesce to form larger cracks and then fractures. The research reported here has advanced knowledge about these mechanisms through experimental and theoretical work. Experiments were conducted on "model rock" in form of gypsum and on marble as well as some initial work on granite. Innovative experimentation techniques such as high speed video recordings were used. The results showed typical crack propagation and coalescence geometries, which depend on the geometry of preexisting cracks and inclusions, the stress state and the material. Such a systematic classification did not exist so far. Very important also is the fact that it was possible to determine if cracking occurs in tension or shear. This allowed us to develop theoretical (analytical) models representing the cracking processes more accurately. The intellectual merit of the research and of its results is multifold. Most important is the understanding of cracking mechanisms in shear, in tension or combinations. This understanding, which was not available so far, is fundamental and applies to all brittle and semi-brittle materials. On the next higher level is the knowledge of different propagation - and coalescence patterns depending on crack geometry, stress state and material. This involves not only knowing what is physically occurring but also being able to model it analytically, thus forming the basis for predictions. Particularly important is also the successful comparison with some basic theories on the behavior or material, of cracks and of openings/inclusions. The broader impact is substantial: It is now possible to better represent geological processes involving the genesis of fractures (joints) and other discontinuities in rock masses. Even more important is the impact on engineering, for which material behavior and especially the effect of cracking is absolutely essential when analyzing and predicting the performance of engineered structures and of the natural environment affecting such structures. Another part of the broader impact is the educational aspect related to this research: one postdoctoral fellow, two doctoral students, five masters students and five undergraduate students were involved. Related to this is the publications output in the form of 7 papers in refereed journals and 14 papers in other publications (proceedings, thesis).

Project Start
Project End
Budget Start
Budget End
Support Year
Fiscal Year
Total Cost
Indirect Cost
Massachusetts Institute of Technology
United States
Zip Code