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In 1991, my newly formed researchgroupat Berkeley was working
intensely in the area of continuum-level constitutive relationships
that could be obtained in a deductive mannerfrom
microstructuralinformationthroughthemethods of homogenization
theory. Of particular interest was the application of such methods
to structural problems in the blossoming field of micromechanical
devices. In this context it was becoming evident that we needed to
learn to navigate through the continuum/discrete interface. Such
were the circumstances when Vladimir Granik came to visit us at
Berkeley for the first time. It is probably not surprising that we
received with great enthusiasm his offer to join forces and develop
a mechanics .of solid structures that would be based on a discrete
representation of matter. Vladimir had established the foundations
for such an endeavor with his work at Moscow University in the late
1970s. Since that first meeting, and with ever-increasing
enthusiasm, it has been a great privilege for me to collaborate
with Vladimir. We first applied the formalism of what has become
known as "doublet mechanics" to the microstructure-based theory of
failure of solids and worked on the paral- lels and differences
between the doublet approach and homogenization, to- gether with
Kevin Mon and Derek Hansford. Plane elastodynamics followed after
Francesco Maddalena had proposed doublet viscoelesticity. The
consti- tutive relationships in doublet mechanics were laid on a
firm thermodynami- cal foundation through the work of Kevin Mon,
while Miqin Zhang analyzed free boundary effects on multi-scale
plane elastic waves in discrete domains.
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