On Certain Weak Phase Transformations in Multilattices

Abstract

This paper is dedicated to the memory of Clifford Truesdell, to whom I acknowledge my debt and gratitude. I present some recent results of mine on thermomechanics of crystalline solids, a research on which I began working during my stay at The Johns Hopkins University, 1977University, -1979. Then, in the last section, I mention some unusual merits of Truesdell, which I experienced in my scientific career and are not widely known.

On configurational weak phase transitions in graphene

“…Since graphene is a monoatomic 2-net, we distinguish between configurational and structural weak phase changes in line with Pitteri's fundamental work [17]. Configurational are those transitions in which the motif follows the deformation of the skeleton, at least in the beginning [17].…”

“…Group generators are described by tensors R π/3 k , R j , the last tensor describing reflection with respect to the vector j. So, graphene is an essential multilattice in the sense of Pitteri [17]. This stems from Eq.…”

“…Configurational are those transitions in which the motif follows the deformation of the skeleton, at least in the beginning [17]. On the other hand, structural transitions are driven by the deformation of the motif, followed by a suitable consequent skeleton deformation.…”

“…The reduced bifurcation diagram consists of three transcritical bifurcation branches which are unstable. They can be stabilized to produce a subcritical bifurcation [17].…”

“…Starting from the definition of a weak transformation neighborhood, we find bounds on the components of graphene's metric tensor that characterize a weak transformation neighborhood. Section 4 presents the generic scheme of weak phase transitions for multilattices following [4,17]. We first introduce configurational and structural weak phase transitions, and in Sect.…”