Details
| Original language | English |
|---|---|
| Article number | 115010 |
| Pages (from-to) | 1015-1031 |
| Number of pages | 17 |
| Journal | Computational mechanics |
| Volume | 75 |
| Issue number | 3 |
| Early online date | 14 Oct 2024 |
| Publication status | Published - Mar 2025 |
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
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Engineering(all)
- Mechanical Engineering
- Engineering(all)
- Ocean Engineering
- Mathematics(all)
- Applied Mathematics
- Engineering(all)
- Computational Mechanics
- Computer Science(all)
- Computational Theory and Mathematics
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In: Computational mechanics, Vol. 75, No. 3, 115010, 03.2025, p. 1015-1031.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On constraint-conforming numerical discretizations in constitutive material modeling
AU - Bode, T.
AU - Soleimani, M.
AU - Erdogan, C.
AU - Hackl, K.
AU - Wriggers, P.
AU - Junker, P.
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2025/3
Y1 - 2025/3
N2 - 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.
AB - 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.
KW - Backward-Euler
KW - Finite plasticity
KW - Hamilon principle
KW - Phase transformation
UR - http://www.scopus.com/inward/record.url?scp=105001075981&partnerID=8YFLogxK
U2 - 10.1007/s00466-024-02548-3
DO - 10.1007/s00466-024-02548-3
M3 - Article
VL - 75
SP - 1015
EP - 1031
JO - Computational mechanics
JF - Computational mechanics
SN - 0178-7675
IS - 3
M1 - 115010
ER -