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A consistent time FE-method for large strain elasto-plasto-dynamics

Mohr, Rouven; Menzel, Andreas LU and Steinmann, Paul (2008) In Computer Methods in Applied Mechanics and Engineering 197(33-40). p.3024-3044
Abstract
In the present paper energy-consistent momentum-conserving time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics referred to as `ECMC-cG methods' are developed. In this context, the entire discretisation procedure of the global equations of motion is based on Galerkin methods in space and time, whereby special emphasis is placed on the desired conservation properties related to the approximation of time-integrals. To guarantee energy-consistency also for higher-order Finite Elements in time, a thermodynamically motivated `enhanced stress tensor', which defines a non-standard quadrature rule, is derived for elasto-plastic material behaviour. Concerning the integration of the local evolution equations in... (More)
In the present paper energy-consistent momentum-conserving time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics referred to as `ECMC-cG methods' are developed. In this context, the entire discretisation procedure of the global equations of motion is based on Galerkin methods in space and time, whereby special emphasis is placed on the desired conservation properties related to the approximation of time-integrals. To guarantee energy-consistency also for higher-order Finite Elements in time, a thermodynamically motivated `enhanced stress tensor', which defines a non-standard quadrature rule, is derived for elasto-plastic material behaviour. Concerning the integration of the local evolution equations in time, exemplarily, a well-established first-order accurate exponential update is applied and adapted according to the global time-stepping scheme based on linear Finite Elements in time. The performance of the resulting scheme is demonstrated by means of several representative numerical examples, whereby it is shown that global energy-consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Computer Methods in Applied Mechanics and Engineering
volume
197
issue
33-40
pages
3024 - 3044
publisher
Elsevier
external identifiers
  • wos:000257666400023
  • scopus:44749090960
ISSN
0045-7825
DOI
10.1016/j.cma.2008.02.002
language
English
LU publication?
yes
id
581ac03e-812a-46e3-84a5-503af488fb65 (old id 1515220)
date added to LUP
2009-12-10 11:03:21
date last changed
2017-01-01 06:27:23
@article{581ac03e-812a-46e3-84a5-503af488fb65,
  abstract     = {In the present paper energy-consistent momentum-conserving time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics referred to as `ECMC-cG methods' are developed. In this context, the entire discretisation procedure of the global equations of motion is based on Galerkin methods in space and time, whereby special emphasis is placed on the desired conservation properties related to the approximation of time-integrals. To guarantee energy-consistency also for higher-order Finite Elements in time, a thermodynamically motivated `enhanced stress tensor', which defines a non-standard quadrature rule, is derived for elasto-plastic material behaviour. Concerning the integration of the local evolution equations in time, exemplarily, a well-established first-order accurate exponential update is applied and adapted according to the global time-stepping scheme based on linear Finite Elements in time. The performance of the resulting scheme is demonstrated by means of several representative numerical examples, whereby it is shown that global energy-consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts.},
  author       = {Mohr, Rouven and Menzel, Andreas and Steinmann, Paul},
  issn         = {0045-7825},
  language     = {eng},
  number       = {33-40},
  pages        = {3024--3044},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {A consistent time FE-method for large strain elasto-plasto-dynamics},
  url          = {http://dx.doi.org/10.1016/j.cma.2008.02.002},
  volume       = {197},
  year         = {2008},
}