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Objective algorithms for integrating hypoelastic constitutive relations based on corotational stress rates

Record Type:	Electronic resources : Monograph/item
Title/Author:	Objective algorithms for integrating hypoelastic constitutive relations based on corotational stress ratesby Sergey Korobeynikov, Alexey Larichkin.
Author:	Korobeynikov, Sergey.
other author:	Larichkin, Alexey.
Published:	Cham :Springer Nature Switzerland :2023.
Description:	xiii, 107 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Continuum mechanicsMathematics.
Online resource:	https://doi.org/10.1007/978-3-031-29632-1
ISBN:	9783031296321$q(electronic bk.)

Objective algorithms for integrating hypoelastic constitutive relations based on corotational stress rates
Korobeynikov, Sergey.

Objective algorithms for integrating hypoelastic constitutive relations based on corotational stress rates[electronic resource] /by Sergey Korobeynikov, Alexey Larichkin. - Cham :Springer Nature Switzerland :2023. - xiii, 107 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in continuum mechanics,2625-1337. - SpringerBriefs in continuum mechanics..

1. Introduction -- 2. Preliminaries -- 3. Incremental tensors and the incremental objectivity of tensors -- 4. Incrementally objective algorithms for integrating CRs for Hooke-like hypoelastic models in the Eulerian form -- 5. Absolutely objective algorithms for integrating CRs for Hooke-like hypoelastic models -- 6. Comparative analysis and veriﬁcation of objective algorithms -- 7. Concluding remarks. A. Flowcharts of objective algorithms for integrating hypoelastic constitutive relations -- B. Algorithms for determining the polar decomposition -- C. The Rodrigues formula for determining an incremental rotation tensor -- Index.

This book provides readers with a deep understanding of the use of objective algorithms for integration of constitutive relations (CRs) for Hooke-like hypoelasticity based on the use of corotational stress rates. The purpose of objective algorithms is to perform the step-by-step integration of CRs using fairly large time steps that provide high accuracy of this integration in combination with the exact reproduction of superimposed rigid body motions. Since Hooke-like hypoelasticity is included as a component in CRs for elastic-inelastic materials (e.g., in CRs for elastic-plastic materials), the scope of these algorithms is not limited to hypoelastic materials, but extends to many other materials subjected to large deformations. The authors performed a comparative analysis of the performance of most currently available objective algorithms, provided some recommendations for improving the existing formulations of these algorithms, and presented new formulations of the so-called absolutely objective algorithms. The proposed book will be useful for beginner researchers in the development of economical methods for integrating elastic-inelastic CRs, as well as for experienced researchers, by providing a compact overview of existing objective algorithms and new formulations of these algorithms. The book will also be useful for developers of computer codes for implementing objective algorithms in FE systems. In addition, this book will also be useful for users of commercial FE codes, since often these codes are so-called black boxes and this book shows how to test accuracy of the algorithms of these codes for integrating elastic-inelastic CRs in modeling large rotations superimposed on the uniform deformation of any sample.

ISBN: 9783031296321$q(electronic bk.)

Standard No.: 10.1007/978-3-031-29632-1doiSubjects--Topical Terms:

376796
Continuum mechanics
--Mathematics.

LC Class. No.: QA808.2 / .K67 2023

Dewey Class. No.: 531.7

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505 0 $a 1. Introduction -- 2. Preliminaries -- 3. Incremental tensors and the incremental objectivity of tensors -- 4. Incrementally objective algorithms for integrating CRs for Hooke-like hypoelastic models in the Eulerian form -- 5. Absolutely objective algorithms for integrating CRs for Hooke-like hypoelastic models -- 6. Comparative analysis and veriﬁcation of objective algorithms -- 7. Concluding remarks. A. Flowcharts of objective algorithms for integrating hypoelastic constitutive relations -- B. Algorithms for determining the polar decomposition -- C. The Rodrigues formula for determining an incremental rotation tensor -- Index.
520 $a This book provides readers with a deep understanding of the use of objective algorithms for integration of constitutive relations (CRs) for Hooke-like hypoelasticity based on the use of corotational stress rates. The purpose of objective algorithms is to perform the step-by-step integration of CRs using fairly large time steps that provide high accuracy of this integration in combination with the exact reproduction of superimposed rigid body motions. Since Hooke-like hypoelasticity is included as a component in CRs for elastic-inelastic materials (e.g., in CRs for elastic-plastic materials), the scope of these algorithms is not limited to hypoelastic materials, but extends to many other materials subjected to large deformations. The authors performed a comparative analysis of the performance of most currently available objective algorithms, provided some recommendations for improving the existing formulations of these algorithms, and presented new formulations of the so-called absolutely objective algorithms. The proposed book will be useful for beginner researchers in the development of economical methods for integrating elastic-inelastic CRs, as well as for experienced researchers, by providing a compact overview of existing objective algorithms and new formulations of these algorithms. The book will also be useful for developers of computer codes for implementing objective algorithms in FE systems. In addition, this book will also be useful for users of commercial FE codes, since often these codes are so-called black boxes and this book shows how to test accuracy of the algorithms of these codes for integrating elastic-inelastic CRs in modeling large rotations superimposed on the uniform deformation of any sample.
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