  In this paper, we investigate the inherent physical and mathematical
character of higher gradient theories, in which the strain or distortion
gradients are considered as the fundamental measures of deformation. Contrary
to common belief, the first or higher strain or distortion gradients are not
proper measures of deformation. Consequently, their corresponding energetically
conjugate stresses are non-physical and cannot represent the state of internal
stresses in the continuum. Furthermore, the governing equations in these
theories do not describe the motion of infinitesimal elements of matter
consistently. For example, in first strain gradient theory, there are nine
governing equations of motion for infinitesimal elements of matter at each
point; three force equations, and six unsubstantiated artificial moment
equations that violate Newton's third law of action and reaction and the
angular momentum theorem. This shows that the first strain gradient theory
(F-SGT) is not an extension of rigid body mechanics, which then is not
recovered in the absence of deformation. The inconsistencies of F-SGT and other
higher gradient theories also manifest themselves in the appearance of strains,
distortions or their gradients as boundary conditions and the requirement for
many material coefficients in the constitutive relations.
