Elasticity theory of materials with long range cohesive forces

Abstract

The strain energy of a deformed material with spatial interaction can be written either in a differential (multipolar) form, i.e. as a single volume integral containing displacement gradients up to infinite order, or in an integral (non-local) form, e.g. as a double volume integral summing up the interactions of pairs of mass elements. The linear theory is derived from lattice theory and the following insights have been gained:1.(1) The differential theory, though in principle applicable to any (analytic) elastic long range problem, is mainly convenient in describing range effects on a very small (nearly atomic) scale.2.(2) The effects of the electric cohesive forces can be comprised in the two-point material tensors (kernels) of the non-local theory. In this way, the macroscopical theory becomes purely elastic.3.(3) Van der Waals cohesive forces give rise to elastic range effects under certain inhomogeneous stress conditions, in particular in defect interaction and diffusion problems.