Extended balance of linear momentum from higher gradient stress field theory

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 Lc. 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 L2c 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)