The most frequently used form for the stress at atomic level is based upon the Clausius virial theorem, which determines the stress field applied to the surface of a fixed volume containing interacting particles (atoms). It is essential to recognize that the stress at the location of an atom depends on the details of the interatomic interactions and the positions of interacting neighbours. Hence, the atomic stress is a non-local function of the state of the matter at all points in some vicinity of the reference atom, in contrast to the local stress field used in classical continuum theories.

It seems that the relationship between local displacements of atoms and the strain tensor is not as ambiguous as the concept of atomic stress. Strain measure is a relative quantity and one needs two configurations, the reference and the present, in order to define the local atomic strain which should provide detailed local information about kinematics of the atom in relation to its neighbours.

The atomic strain tensor is applied to investigate deformation of regular and disordered molecular systems. As classical continuum mechanics is inherently size-independent, inclusion of atomic strain gradients is used to analyse and predict the mechanical behaviour of nanomaterials in presence of size effects. It is shown that disordered systems exhibit significant nonaffine deformations. The characteristic length scale over which the nonaffine field is correlated serves as a lower limit beyond which classical continuum elasticity cannot be applied. The high nonaffinity of disordered (amorphous) nanomaterials possibly stems from a group of strongly bonded atoms behaving as a unit and therefore high moment stresses may result. This effect can be captured by the atomic strain gradient tensor in a way similar to the strain gradient elasticity solution.

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