Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge-Kutta integration scheme
(2013) In International Journal of Damage Mechanics 22(1). p.68-94- Abstract
- Abstract in Undetermined
This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen (1999) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of... (More) - Abstract in Undetermined
This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen (1999) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge--Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge--Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge--Kutta scheme over the implicit Euler scheme is reduced. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2065079
- author
- Borgqvist, Eric LU and Wallin, Mathias LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- damage evolution, differential algebraic equation, diagonal implicit, Runge-Kutta, numerical integration
- in
- International Journal of Damage Mechanics
- volume
- 22
- issue
- 1
- pages
- 68 - 94
- publisher
- SAGE Publications
- external identifiers
-
- wos:000314187500005
- scopus:84873181297
- ISSN
- 1056-7895
- DOI
- 10.1177/1056789511433341
- language
- English
- LU publication?
- yes
- id
- c6b8e9b2-7212-473c-acc9-8755a534fc21 (old id 2065079)
- date added to LUP
- 2016-04-01 09:51:18
- date last changed
- 2022-04-03 23:58:25
@article{c6b8e9b2-7212-473c-acc9-8755a534fc21,
abstract = {{Abstract in Undetermined<br/>This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen (1999) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge--Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge--Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge--Kutta scheme over the implicit Euler scheme is reduced.}},
author = {{Borgqvist, Eric and Wallin, Mathias}},
issn = {{1056-7895}},
keywords = {{damage evolution; differential algebraic equation; diagonal implicit; Runge-Kutta; numerical integration}},
language = {{eng}},
number = {{1}},
pages = {{68--94}},
publisher = {{SAGE Publications}},
series = {{International Journal of Damage Mechanics}},
title = {{Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge-Kutta integration scheme}},
url = {{http://dx.doi.org/10.1177/1056789511433341}},
doi = {{10.1177/1056789511433341}},
volume = {{22}},
year = {{2013}},
}