Abstract
The compatibility of the hypoelastic-Synge (isotropic case) and hypoelastic-Carter and Quintana (fully isotropic case) almost-thermodynamic material schemes with the relativistic incompressibility condition, given by Ferrando and Olivert, is analyzed. The behavior of those schemes in Born-rigid motion is also studied and an additional stipulation is joined to the Born rigidity concept. This requisite leads to the vanishing of the relativistic stress tensor spatial variation and, in hypoelastic-Carter and Quintana and hypoelastic-Maugin almost-thermodynamic material schemes, leads to the absence of mechanical power originated by internal rotation. The rigidity definition that is proposed remains valid for more general almost-thermodynamic material schemes, as far as the compatibility with the incompressibility condition quoted above is concerned.
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