Nonlocal balance of angular momentum from stress field analysis

Abstract

AbstractNonlocal theories drop the principle of local action such that the stress field in the contiguity of a continuum point is represented by a nonlinear tensor‐function. Therefore, its power series expansion has higher order terms and the balance of linear momentum becomes nonlocal, see [1, 2]. Here, we focus on the balance of angular momentum by considering up to quadratic terms in the approximation of the stress field. This yields nonlinear tractions on the surface of spatial unit cells, where an algebraic formula for the couple stress tensor can be found. However, couple stress is an auxiliary quantity, which is usually motivated as work conjugated to curvature. With help of some algebra in ℝ3 × ℝ3 × ℝ3 it is found, that the curl of the stress field rules the nonlocal balance of angular momentum. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)