Geodesic
Stress-strain measures used in the ANSYS package to solve elastoplastic problems at finite strains
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2017), pp. 31-36
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It is shown that the Dienes (or the Green–McInnis–Naghdi) stress rate is used as an objective stress rate of the Cauchy stress for solving elastic-plastic problems in the ANSYS program instead of the Jaumann stress rate announced in the ANSYS Theory Reference. The strain tensor is not the logarithmic or Hencky strain measure as is announced in the ANSYS Theory Reference, but it is a right nonholonomic strain tensor such that the left tensor is generated by the Dienes derivative. 
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N. V. Ovchinnikova. Stress-strain measures used in the ANSYS package to solve elastoplastic problems at finite strains. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2017), pp. 31-36. http://geodesic.mathdoc.fr/item/VMUMM_2017_5_a4/

[1] ANSYS Academic Teaching Introductory, Release 16.2, Help System, Mechnical APDL, Theory Reference, Ch. 3. Structures with Geometric Nonlinearities, ANSYS, Inc., 2015

[2] Hughes T.J.R., “Numerical implementation of constitutive models: rate-independent deviatoric plasticity”, Theoretical foundation for large-scale computations for nonlinear material behavior, eds. S. Nemat-Nasser, R.J. Asaro, G.A. Hegemier, Martinus Nijhoff Publishers, Dordrecht, Netherlands, 1984

[3] Brovko G.L., “Nekotorye podkhody k postroeniyu opredelyayuschikh sootnoshenii plastichnosti pri bolshikh deformatsiyakh”, Uprugost i neuprugost, Izd-vo MGU, M., 1987, 68–81

[4] Tolokonnikov L.A., Markin A.A., “Opredelyayuschie sootnosheniya pri konechnykh deformatsiyakh”, Problemy mekhaniki deformiruemogo tverdogo tela, Mezhvuz. sb. tr. Kalinin. politekh. in-ta, Izd-vo KGU, Kalinin, 1986, 49–57

[5] Markin A.A., Sokolova M.Yu., Termomekhanika uprugoplasticheskogo deformirovaniya, Fizmatlit, M., 2013

[6] Dienes J.K., “On the analysis of rotation and stress rate in deforming bodies”, Acta Mech., 32 (1979), 217–232 | DOI | MR | Zbl

[7] Simo J.C., Hughes T.J.R., Computational Inelasticity, Springer-Verlag, NY, 1998 | MR | Zbl

[8] Ovchinnikova N.V., Muravlev A.V., “Otsenka tochnosti vychisleniya inkrementalnymi metodami konechnykh uprugoplasticheskikh deformatsii v paketakh ANSYS i QFORM7”, KhI Vseros. s'ezd po fundamentalnym problemam teoreticheskoi i prikladnoi mekhaniki, Sb. tr. (Kazan, 20–24 avgusta 2015 g.), Izd-vo Kazan. (Privolzhskogo) feder. un-ta, Kazan, 2015, 2825–2827

[9] Ovchinnikova N.V., Muravlev A.V., “O primenenii mer konechnykh deformatsii v paketakh ANSYS i QFORM7”, Uprugost i neuprugost, Mat-ly Mezhdunar. nauch. simp. po problemam mekhaniki deformiruemykh tel, posvyaschennogo 105-letiyu so dnya rozhdeniya A.A. Ilyushina (g. Moskva, 20–21 yanvarya 2016), Izd-vo MGU, M., 2016, 233–236

[10] Johnson G.C., Bammann D.J., “A discussion of stress rates in finite deformation problems”, Int. J. Solids and Struct., 20:8 (1984), 725–737 | DOI | MR | Zbl