Geodesic
Kinematics of finite elastoplastic deformations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 16-30

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We review various approaches to decomposition of total strains on elastic and nonelastic (plastic) components in a multiplicative representation of the deformation gradient tensor. We briefly describe the kinematics of finite strains and arbitrary flows. We show that the products of elastic and plastic principal stretches define full principal stretches. We describe two groups of techniques for decomposing strains and their rates on elastic and nonelastic components. Methods of the first group additively decompose specially constructed tensors defined in a uniform basis (initial, current, or “intermediate” one). Methods of the second group use some relation connecting tensors that describe elastic and plastic strains. We adduce an example of obtaining constitutive equations for elastoplastic continuums under large deformations from equations of thermodynamics.
Keywords: finite elastoplastic strains, material and spatial tensors, additive representation of deformation tensors, principal stretches
Mots-clés : multiplicative decomposition of deformation gradient, principal directions. 
@article{IVM_2010_7_a1,
     author = {A. I. Golovanov},
     title = {Kinematics of finite elastoplastic deformations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {16--30},
     publisher = {mathdoc},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_7_a1/}
}
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A. I. Golovanov. Kinematics of finite elastoplastic deformations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 16-30. http://geodesic.mathdoc.fr/item/IVM_2010_7_a1/