The current use of complex materials in nanotechnology and industrial
engineering has led to a number of intricate problems in mechanics, and
the macroscopic behavior of such materials often depends critically on
their substructures. This work, written by leading mathematicians and
engineers, features a broad range of topics that offer both experimental
results and clear, detailed answers to fundamental questions about the
general formulation of multifield theories within the context of
modeling material substructures. Applied mathematicians, mechanical and
structural engineers, material scientists, graduate students, and
researchers in the above areas will benefit from the work and may find
suggestions for further research in its rich collection of open
problems.