On constraint-conforming numerical discretizations in constitutive material modeling

authored by: T. Bode, M. Soleimani, C. Erdogan, K. Hackl, P. Wriggers, P. Junker
Abstract: For the modelling of complex materials, internal variables are usually introduced which characterize the microstructural state. Then, evolution equations describe the change of the internal variables due to varying external loading conditions. These equations can be derived, for instance, on the basis of variational principles. The consideration of characteristic observations, such as the preservation of the volume during a change in the microstructural state, can significantly improve the accuracy of the evolution equations. We present a Hamilton principle that provides a unique way to derive evolution equations that obey holonomic constraints and opens up new possibilities for their algorithmic treatment. This is demonstrated for isochoric finite plasticity and phase transformation based on Backward-Euler time discretization. The models presented are efficient and are characterized by simple implementation compared to the exponential map, for example, without suffering a loss of accuracy due to unfulfilled constraints.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computational mechanics
Volume: 75
Pages: 1015-1031
No. of pages: 17
ISSN: 0178-7675
Publication date: 03.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mathematics, Mechanical Engineering, Ocean Engineering, Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-024-02548-3 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{e7d56fdaa18a4421b6ce1cabcf57db3d,
title = "On constraint-conforming numerical discretizations in constitutive material modeling",
abstract = "For the modelling of complex materials, internal variables are usually introduced which characterize the microstructural state. Then, evolution equations describe the change of the internal variables due to varying external loading conditions. These equations can be derived, for instance, on the basis of variational principles. The consideration of characteristic observations, such as the preservation of the volume during a change in the microstructural state, can significantly improve the accuracy of the evolution equations. We present a Hamilton principle that provides a unique way to derive evolution equations that obey holonomic constraints and opens up new possibilities for their algorithmic treatment. This is demonstrated for isochoric finite plasticity and phase transformation based on Backward-Euler time discretization. The models presented are efficient and are characterized by simple implementation compared to the exponential map, for example, without suffering a loss of accuracy due to unfulfilled constraints.",
keywords = "Backward-Euler, Finite plasticity, Hamilon principle, Phase transformation",
author = "T. Bode and M. Soleimani and C. Erdogan and K. Hackl and P. Wriggers and P. Junker",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2025",
month = mar,
doi = "10.1007/s00466-024-02548-3",
language = "English",
volume = "75",
pages = "1015--1031",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "3",
}