An asymmetric theory of nonlocal elasticity—Part 1. Quasicontinuum theory

In this article\ an asymmetric theory of nonlocal elasticity is developed on the basis of three dimensional atomic lattice model\ the Galileo invariance for constitutive equations and by use of Fourier transformation of generalized function and energy method[ It is shown that nonlocal characteristic functions "or constitutive parameters of internal elastic energy# can be explicitly expressed in terms of interacting forces connecting atoms\ and the general model of nonlocal theory with rotation e}ects is asymmetric[ Both symmetric stress and anti!symmetric stress is a nonlocal function of strain and local rotation for anisotropic materials[ For isotropic materials\ symmetric stress is only a nonlocal function of strain\ while antisymmetric stress is only a nonlocal function of local rotation