A note on the higher order strain and stress tensors within deformation gradient elasticity theories: Physical interpretations and comparisons

•Physical meaning of double and triple stresses.•Tensor representation of double and triple stresses.•Comparison of distortion gradient and strain gradient based elasticity theories.•Applicability of Mindlin rule for double and triple stresses. Higher order strain and stress tensors encompassed within gradient elasticity theories are discussed with a particular concern to the physical meaning of double and triple stresses. A single rule is shown to hold for the physical interpretation of the indices of a higher order stress tensor both within distortion gradient and strain gradient theories, whereas the analogous Mindlin’s rule holds only within distortion gradient theories. Double and triple stresses are discussed separately with the aid of simple illustrative examples. A corrigendum to a previous paper by the author (IJSS 50 (2013) 3749–3765) is also presented.