The last few decades have witnessed the introduction of new paradigms into the field of solid mechanics. The "rational mechanics" era gave way to a fruitful period characterized by a desire to root our understanding of material behavior directly in "micromechanics." This inevitably requires spanning multiple length scales. Instead of proceeding phenomenologically, the principles and tools of mechanics are brought to bear on phenomena occurring at the microscale. The observer then steps back and the microscopic features blur into macroscopic fields which are governed by a different set of "effective" laws.
The determination of these effective properties from first principles is one of the principal objectives of micromechanics. A related endeavor is the use of the knowledge base thus acquired for the design of microstructures resulting in improved material properties. The feasibility of this program has been greatly enhanced by developments in microscopy, which enable the kind of precise observations and measurements required to guide modelling, and to a considerable extent by developments in computer hardware and software. Indeed, the advent of fast digital computers has furnished, for the first time in the history of mechanics, the computing power required for such detailed large-scale simulations as are required to span multiple length scales.
Because of the broad scope of the field, micromechanics cannot be readily encapsulated as a self-contained and unified formal theory. Instead, in this short course I will endeavor to convey a sense of the field by way of example, with particular emphasis on multiple-scale problems and micromechanical models of material behavior. Examples considered include: the bridging of atomistic and continuum scales, with application to nanoindentation and the brittle-to-ductile transition; the development of dislocation-based constitutive relations for pure metallic crystals and intermetallic compounds, with applications to fracture of single crystals and bicrystals; the simulation of non-planar three-dimensional crack growth at the microscale, with application to mixed mode I-III effective behavior and crack trapping and bridging in fiber-reinforced composites; and the direct micromechanical simulation of fragmentation of brittle solids and subsequent flow of the comminuted phase.