Nonlocal balance of angular momentum from stress field analysis

Nonlocal balance of angular momentum from stress field analysis Nonlocal 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Nonlocal balance of angular momentum from stress field analysis

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710137
Publisher site
See Article on Publisher Site

Abstract

Nonlocal 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)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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