Advances in Doublet Mechanics

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.