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=== Kinematics of multiplicative plasticity ===
The concept of multiplicative decomposition of the deformation gradient into elastic and plastic parts was first proposed independently by B. A. Bilby,<ref>{{Citation|last1=Bilby|first1=B. A.|last2=Bullough|first2=R.|last3=Smith|first3= E.|year=1955|title= Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry|journal= Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences|volume= 231|
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\boldsymbol{F} = \boldsymbol{F}^e\cdot\boldsymbol{F}^p
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\boldsymbol{M} := \tfrac{1}{2}(\boldsymbol{C}^e\cdot\boldsymbol{S} + \boldsymbol{S}\cdot\boldsymbol{C}^e)
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where '''''S''''' is the [[stress measures|second Piola-Kirchhoff stress]]. A possible hyperelastic model in terms of the logarithmic strain is <ref>{{Citation|last=Anand|first= L.|year=1979|title= On H. Hencky's approximate strain-energy function for moderate deformations|journal= ASME Journal of Applied Mechanics|volume= 46|pages= 78.|bibcode=1979JAM....46...78A|doi=10.1115/1.3424532}}</ref>
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\boldsymbol{M} = \frac{\partial W}{\partial \boldsymbol{E}^e} = J\,\frac{dU}{dJ} + 2\mu\,\text{dev}(\boldsymbol{E}^e)
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