On Potential Energy Shifts in Hyperelastic Energy-Momentum Tensors

Abstract

The invariance of the so-called energy-momentum format of the (spatial motion) Cauchy and the (material motion) Eshelby stress tensors of hyperelasticity is discussed with respect to shifts of the potential energy density. As an noteworthy result it turns out that the duality of the spatial and the material motion problem renders the corresponding energy-momentum tensors either invariant or equipped with an additional pressure-like contribution, respectively. This additional pressure like contribution captures the different total potential energy content due to the shift in potential energy density.