Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms...

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Autores principales:	Peter Trusov, Alexey Shveykin, Nikita Kondratev
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	crystal plasticity multilevel models large strain motion decomposition constitutive law anisotropic materials Crystallography QD901-999
Acceso en línea:	https://doaj.org/article/eb980a068fe34dcb91dd46f249f4821b
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spelling	oai:doaj.org-article:eb980a068fe34dcb91dd46f249f4821b2021-11-25T17:19:18ZSome Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants10.3390/cryst111113922073-4352https://doaj.org/article/eb980a068fe34dcb91dd46f249f4821b2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-4352/11/11/1392https://doaj.org/toc/2073-4352In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.Peter TrusovAlexey ShveykinNikita KondratevMDPI AGarticlecrystal plasticitymultilevel modelslarge strainmotion decompositionconstitutive lawanisotropic materialsCrystallographyQD901-999ENCrystals, Vol 11, Iss 1392, p 1392 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	crystal plasticity multilevel models large strain motion decomposition constitutive law anisotropic materials Crystallography QD901-999
spellingShingle	crystal plasticity multilevel models large strain motion decomposition constitutive law anisotropic materials Crystallography QD901-999 Peter Trusov Alexey Shveykin Nikita Kondratev Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
description	In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.
format	article
author	Peter Trusov Alexey Shveykin Nikita Kondratev
author_facet	Peter Trusov Alexey Shveykin Nikita Kondratev
author_sort	Peter Trusov
title	Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
title_short	Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
title_full	Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
title_fullStr	Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
title_full_unstemmed	Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants
title_sort	some issues on crystal plasticity models formulation: motion decomposition and constitutive law variants
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/eb980a068fe34dcb91dd46f249f4821b
work_keys_str_mv	AT petertrusov someissuesoncrystalplasticitymodelsformulationmotiondecompositionandconstitutivelawvariants AT alexeyshveykin someissuesoncrystalplasticitymodelsformulationmotiondecompositionandconstitutivelawvariants AT nikitakondratev someissuesoncrystalplasticitymodelsformulationmotiondecompositionandconstitutivelawvariants
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Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

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