Differential Geometry and Continuum Mechanics by Gui-Qiang G. Chen Michael Grinfeld & R. J. Knops

Author:Gui-Qiang G. Chen, Michael Grinfeld & R. J. Knops
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.5.26)

and the product is defined by

(6.5.27)

for all vectors .

The conservation law (6.5.25), related to configurational forces which for microstructure are studied by Mariano [Mar00], generalises that previously employed to investigate crack propagation and the J-integral introduced by Rice [Ric68]; see also [MT92].

When the material is homogeneous and in static equilibrium under zero source terms, we have

(6.5.28)

and the conservation law (6.5.25) reduces to

(6.5.29)

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