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Extended balance of linear momentum from higher gradient stress field theory
Author(s) -
Münch Ingo,
Wöhler Franziska
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610192
Subject(s) - momentum (technical analysis) , mathematics , series (stratigraphy) , taylor series , mathematical analysis , balance (ability) , field (mathematics) , stress field , physics , finite element method , pure mathematics , thermodynamics , medicine , paleontology , finance , economics , physical medicine and rehabilitation , biology
We present the equation of linear momentum considering higher gradients for stress and body force. Both are approximated via Taylor series expansion within a finite Cauchy cube of dimensions L c . Whereas linear terms of the series expansion result to the classical balance of linear momentum, terms up to third order yield an extended balance equation. The extension includes an internal length scale L 2 c caused by surface integrals on the cube. The approach makes use of Cauchy's theorem and standard Newtonian mechanics but constitutive assumptions are not applied. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)