Flow plasticity theory: Difference between revisions

Revision as of 01:19, 22 August 2013

Revision as of 02:15, 22 August 2013

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\boldsymbol{E}^e := \tfrac{1}{2}\ln\boldsymbol{C}^e \,.

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The symmetrized [[Mandel stress]] tensor is a convenient stress measure for finite plasticity and is defined as

:<math>

\boldsymbol{M} := \tfrac{1}{2}(\boldsymbol{C}^e\cdot\boldsymbol{S} + \boldsymbol{S}\cdot\boldsymbol{C}^e)

</math>

where '''''S''''' is the [[stress measures|second Piola-Kirchhoff stress]]. FromA apossible polarhyperelastic decompositionmodel in terms of the elasticlogarithmic deformationstrain gradient,is we have '''''F'''''<sup>e</supref>{{Citation|last=Anand|first= L.|year=1979|title= '''''R'''''^{eOn H.}Hencky'''''U'''''<sup>es approximate strain-energy function for moderate deformations|journal= ASME Journal of Applied Mechanics|volume= 46|pages= 78.}}</supref>

:<math>

\boldsymbol{M} = \frac{\partial W}{\partial \boldsymbol{E}^e} = J\,\frac{dU}{dJ} + 2\mu\,\text{dev}(\boldsymbol{E}^e)

</math>

where ''W'' is a strain energy density function, ''J'' = det('''''F'''''), ''μ'' is a modulus, and "dev" indicates the deviatoric part of a tensor.

== References ==