Journal of Mechanics of Materials and Structures vol. 5 (2010 ... - MSP

710 BAHATTIN KILIC AND ERDOGAN MADENCI
Figure 1. Pairwise interaction of a material point with its neighboring points.
be viewed as a bond force between the material points. The present study utilizes the response function
described in [Kilic 2008], which can be written as
f (η, ξ) =
ξ + η 9k
µ(ξ, t) e−(|ξ|/l)2 s, (2)
|ξ + η| πl 4
in which k is the bulk modulus and l is the internal length, which is the measure of nonlocal behavior.
The locality of interactions depends on the internal length l and interactions become more local with
decreasing internal length, as shown in Figure 2. The relative position, ξ, can be expressed as ξ = x ′ − x
in the reference configuration, as illustrated in Figure 3. The relative displacement, η, can be written as
Figure 2. Effect of internal length on the locality of interactions.