Stress and deformation in soft elastic bodies due to intermolecular forces

Intermolecular interaction within one and between two incompressible, soft elastic bodies is studied at a continuous level. We show that the macroscopic effect of the interaction can be characterized by a deformation-dependent Maxwell stress. The divergence of the Maxwell stress gives the body force, while the inner product of it with the outward normal of a body generates the surface traction. Accordingly, we can replace the contribution of intermolecular forces to the deformation and stress in the body by that of either the body force or the surface traction. Both approaches are proved to be equivalent, in the sense that the resulting displacements are the same and the stresses are linked by an exact correspondence relation. If the deformation induced by the interaction is small, the equations are simplified up to the first order of the displacement gradient. Two examples are given as well to illustrate some features of local stress distribution in a body caused by self and other-body interactions.