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Consistent elastoplastic cohesive zone model at finite deformations – Variational formulation

Heitbreder, Tim; Ottosen, Niels Saabye LU ; Ristinmaa, Matti LU and Mosler, Jörn (2017) In International Journal of Solids and Structures 106-107. p.284-293
Abstract

Cohesive zone models based on classical interface-type formulations at finite deformations are subjected to fundamental physical principles such as thermodynamical consistency, balance equations and material frame indifference. However, these restraints are often ignored and in that respect such formulations are inconsistent. By way of contrast, a consistent cohesive zone framework suitable for the analysis of localized elastoplastic deformations which only depends on the displacement jump was recently advocated in Ottosen et al. (2015). A certain subclass of this consistent framework is analyzed here, further extended and finally, an efficient numerical implementation is proposed. Conceptually, the considered cohesive zone model is a... (More)

Cohesive zone models based on classical interface-type formulations at finite deformations are subjected to fundamental physical principles such as thermodynamical consistency, balance equations and material frame indifference. However, these restraints are often ignored and in that respect such formulations are inconsistent. By way of contrast, a consistent cohesive zone framework suitable for the analysis of localized elastoplastic deformations which only depends on the displacement jump was recently advocated in Ottosen et al. (2015). A certain subclass of this consistent framework is analyzed here, further extended and finally, an efficient numerical implementation is proposed. Conceptually, the considered cohesive zone model is a fiber-like model where the fiber direction is defined by the direction of the displacement discontinuity. A novel unloading model is advocated where the key idea is to assign a vanishing bending stiffness to the fibers and they therefore buckle when compressive stresses are initiated. Following ideas known from wrinkling in membranes, it is shown that the resulting framework can be rewritten into a variationally consistent format such that all unknowns follow jointly from minimizing a time-dependent potential whose discretization leads to an efficient implementation in terms of an efficient variational constitutive update. The physical properties of the final constitutive framework are analyzed by means of numerical examples. This analysis shows that although the framework is based on elastoplasticity, it predicts for the L-shaped structure investigated a mechanical response similar to that of damage theory even during unloading.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Balance laws, Cohesive zone modeling, Elastoplastic finite deformation, Fiber model, Unloading criterion, Variational constitutive update
in
International Journal of Solids and Structures
volume
106-107
pages
10 pages
publisher
Elsevier
external identifiers
  • scopus:85007399909
  • wos:000392889400024
ISSN
0020-7683
DOI
10.1016/j.ijsolstr.2016.10.027
language
English
LU publication?
yes
id
644b1536-a934-493d-bcdd-1fd4b32aebea
date added to LUP
2017-02-06 07:55:14
date last changed
2018-01-07 11:48:23
@article{644b1536-a934-493d-bcdd-1fd4b32aebea,
  abstract     = {<p>Cohesive zone models based on classical interface-type formulations at finite deformations are subjected to fundamental physical principles such as thermodynamical consistency, balance equations and material frame indifference. However, these restraints are often ignored and in that respect such formulations are inconsistent. By way of contrast, a consistent cohesive zone framework suitable for the analysis of localized elastoplastic deformations which only depends on the displacement jump was recently advocated in Ottosen et al. (2015). A certain subclass of this consistent framework is analyzed here, further extended and finally, an efficient numerical implementation is proposed. Conceptually, the considered cohesive zone model is a fiber-like model where the fiber direction is defined by the direction of the displacement discontinuity. A novel unloading model is advocated where the key idea is to assign a vanishing bending stiffness to the fibers and they therefore buckle when compressive stresses are initiated. Following ideas known from wrinkling in membranes, it is shown that the resulting framework can be rewritten into a variationally consistent format such that all unknowns follow jointly from minimizing a time-dependent potential whose discretization leads to an efficient implementation in terms of an efficient variational constitutive update. The physical properties of the final constitutive framework are analyzed by means of numerical examples. This analysis shows that although the framework is based on elastoplasticity, it predicts for the L-shaped structure investigated a mechanical response similar to that of damage theory even during unloading.</p>},
  author       = {Heitbreder, Tim and Ottosen, Niels Saabye and Ristinmaa, Matti and Mosler, Jörn},
  issn         = {0020-7683},
  keyword      = {Balance laws,Cohesive zone modeling,Elastoplastic finite deformation,Fiber model,Unloading criterion,Variational constitutive update},
  language     = {eng},
  month        = {02},
  pages        = {284--293},
  publisher    = {Elsevier},
  series       = {International Journal of Solids and Structures},
  title        = {Consistent elastoplastic cohesive zone model at finite deformations – Variational formulation},
  url          = {http://dx.doi.org/10.1016/j.ijsolstr.2016.10.027},
  volume       = {106-107},
  year         = {2017},
}