A natural vector/matrix notation applied in an efficient and robust return-mapping algorithm for advanced yield functions

A fast and robust stress-integration algorithm is the key to full exploitation of advanced anisotropic yield functions in computational mechanics. Poor global convergence of a direct application of the Newton-Raphson scheme has been rectified by applying line search strategies during the Newton iter...

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Bibliographic Details
Published in:European journal of mechanics, A, Solids Vol. 90; p. 104357
Main Author: Mánik, Tomáš
Format: Journal Article
Language:English
Published: Berlin Elsevier Masson SAS 01.11.2021
Elsevier BV
Subjects:
Algorithms
Continuum plasticity
Exploitation
Finite element method
Mapping
Mathematical analysis
Mathematical models
Matrices (mathematics)
Open source software
Plastic anisotropy
Return mapping algorithm
Robustness
Search methods
Software
Source code
Tensors
Vector notation
Yield function
Plastic anisotropy
Yield function
Continuum plasticity
Return mapping algorithm
Vector notation
ISSN:0997-7538, 1873-7285
Online Access:Get full text
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Summary:A fast and robust stress-integration algorithm is the key to full exploitation of advanced anisotropic yield functions in computational mechanics. Poor global convergence of a direct application of the Newton-Raphson scheme has been rectified by applying line search strategies during the Newton iterations. In this work the line-search approach is further improved by a better first guess. The new algorithm is implemented into a user-defined material subroutine (UMAT) in a finite-element (FE) software and tested. The implementation is made easier and more efficient by a new advantageous vector/matrix notation for symmetric second- and fourth-order tensors, which is the second result of this work. Benefits of this notation are discussed with respect to formulation of continuum-plasticity models as well as their implementations. FE simulations were run to demonstrate the performance of the new implementation, which is available as open-source software via GitLab repository (see Appendix). The new return-mapping algorithm implementation runs equally fast and robust as the simple von Mises and Hill standard implementations in the Abaqus/Standard software. This enables full exploitation of advanced yield functions as the new standard in industrial FE applications. •New advantageous vector/matrix notation for continuum plasticity is proposed.•Efficient and robust implicit return-mapping algorithm is implemented.•Open source UMAT (User-defined material subroutine) is made available.•Use of advanced yield functions in FEM is enabled at lower computational cost.
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ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2021.104357