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An incompatibility tensor-based gradient plasticity formulation—Theory and numerics

Kaiser, Tobias and Menzel, Andreas LU (2019) In Computer Methods in Applied Mechanics and Engineering 345. p.671-700
Abstract

In this work we discuss a gradient plasticity formulation which relies on the introduction of higher-order gradient contributions as additional arguments of the free energy function. These gradients can be interpreted in terms of the local geometrically necessary dislocation density. This gives rise to physically well-motivated kinematic-type hardening models in contrast to purely phenomenological approaches. At the same time, the framework results into a regularisation of the formulation such that localised plastic deformation processes in softening materials, e.g.the formation of shear bands, can be simulated. The employed theory is based on an extended nonlocal form of the Clausius–Duhem inequality, motivated by a possible energy... (More)

In this work we discuss a gradient plasticity formulation which relies on the introduction of higher-order gradient contributions as additional arguments of the free energy function. These gradients can be interpreted in terms of the local geometrically necessary dislocation density. This gives rise to physically well-motivated kinematic-type hardening models in contrast to purely phenomenological approaches. At the same time, the framework results into a regularisation of the formulation such that localised plastic deformation processes in softening materials, e.g.the formation of shear bands, can be simulated. The employed theory is based on an extended nonlocal form of the Clausius–Duhem inequality, motivated by a possible energy exchange between particles at the microstructural level. This gives rise to the balance equation of a nonlocal stress tensor that is found to be work-conjugated to the plastic velocity gradient. The solution of the governing system of partial differential equations is approached by means of a multi-field finite element formulation with the solution of the Karush–Kuhn–Tucker conditions being addressed on a global level by means of Fischer–Burmeister complementary functions. We discuss a specific quadratic energy contribution in terms of the incompatibility, respectively dislocation density tensor that results into well-interpretable contributions to the nonlocal stress field and study the formation of shear bands induced by geometric imperfections as well as the constitutive response at a material interface where the yield limit exhibits a jump discontinuity.

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organization
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type
Contribution to journal
publication status
published
subject
keywords
Back-stress tensor, Finite deformation gradient plasticity, Geometrically necessary dislocations, Localised plastic deformations, Multi-field finite element formulation, Shear band formation
in
Computer Methods in Applied Mechanics and Engineering
volume
345
pages
30 pages
publisher
Elsevier
external identifiers
  • scopus:85058168564
ISSN
0045-7825
DOI
10.1016/j.cma.2018.11.013
language
English
LU publication?
yes
id
07904eb7-2b44-491e-8e99-fae509d76056
date added to LUP
2018-12-17 14:13:15
date last changed
2019-11-13 05:22:55
@article{07904eb7-2b44-491e-8e99-fae509d76056,
  abstract     = {<p>In this work we discuss a gradient plasticity formulation which relies on the introduction of higher-order gradient contributions as additional arguments of the free energy function. These gradients can be interpreted in terms of the local geometrically necessary dislocation density. This gives rise to physically well-motivated kinematic-type hardening models in contrast to purely phenomenological approaches. At the same time, the framework results into a regularisation of the formulation such that localised plastic deformation processes in softening materials, e.g.the formation of shear bands, can be simulated. The employed theory is based on an extended nonlocal form of the Clausius–Duhem inequality, motivated by a possible energy exchange between particles at the microstructural level. This gives rise to the balance equation of a nonlocal stress tensor that is found to be work-conjugated to the plastic velocity gradient. The solution of the governing system of partial differential equations is approached by means of a multi-field finite element formulation with the solution of the Karush–Kuhn–Tucker conditions being addressed on a global level by means of Fischer–Burmeister complementary functions. We discuss a specific quadratic energy contribution in terms of the incompatibility, respectively dislocation density tensor that results into well-interpretable contributions to the nonlocal stress field and study the formation of shear bands induced by geometric imperfections as well as the constitutive response at a material interface where the yield limit exhibits a jump discontinuity.</p>},
  author       = {Kaiser, Tobias and Menzel, Andreas},
  issn         = {0045-7825},
  keyword      = {Back-stress tensor,Finite deformation gradient plasticity,Geometrically necessary dislocations,Localised plastic deformations,Multi-field finite element formulation,Shear band formation},
  language     = {eng},
  pages        = {671--700},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {An incompatibility tensor-based gradient plasticity formulation—Theory and numerics},
  url          = {http://dx.doi.org/10.1016/j.cma.2018.11.013},
  volume       = {345},
  year         = {2019},
}