Elastic Kelvin-Poisson-Poynting solids described through scalar conjugate stress/strain pairs derived from a QR factorization of F Academic Article uri icon

abstract

  • © 2019 Elsevier Ltd The authors (Freed and Zamani, 2018) recently derived a kinematic description for the motion of a deformable body that was constructed out of a Gram-Schmidt factorization of the deformation gradient. Specifically, the metric tensor that associates with a convected co-ordinate system was quantified in terms of the physical attributes that arise from an upper-triangular deconstruction of the deformation gradient. It is within a rectangular, Cartesian, co-ordinate system, created by this Gram-Schmidt factorization, that a frame of reference exists wherein the physical components for convected vector and tensor fields are realized. In this paper the authors derive two sets of thermodynamically admissible stress-strain pairs. They are quantified in terms of physical components extracted from a convected stress and a convected velocity gradient, with elastic models being presented for both sets. The first model supports two modes of deformation: elongation and shear. The second model supports three modes of deformation: dilatation, squeeze and shear. These models are distinguished by their pure- and simple-shear responses. They contain the coupling effects of Lord Kelvin (Thomson, 1878; Poisson, 1827; Poynting, 1909). Furthermore, we show that the Lodge-Meissner (Lodge and Meissner, 1972) effect from rheology and the Poynting (Poynting, 1909) effect from solid mechanics are the same physical phenomenon.

author list (cited authors)

  • Freed, A. D., & Zamani, S.

citation count

  • 6

publication date

  • August 2019