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Spatial representation of evolving anisotropy at large strains

Harrysson, Magnus LU ; Harrysson, Anders LU and Ristinmaa, Matti LU (2007) In International Journal of Solids and Structures 44(10). p.3514-3532
Abstract
A phenomenological model for evolving anisotropy at large strains is presented. The model is formulated using spatial quantities and the anisotropic properties of the material is modeled by including structural variables. Evolution of anisotropy is accounted for by introducing substructural deformation gradients which are linear maps similar to the usual deformation gradient. The evolution of the substructural deformation gradients is governed by the substructural plastic velocity gradients in a manner similar to that for the continuum. Certain topics related to the numerical implementation are discussed and a simple integration scheme for the local constitutive equations is developed. To demonstrate the capabilities of the model it is... (More)
A phenomenological model for evolving anisotropy at large strains is presented. The model is formulated using spatial quantities and the anisotropic properties of the material is modeled by including structural variables. Evolution of anisotropy is accounted for by introducing substructural deformation gradients which are linear maps similar to the usual deformation gradient. The evolution of the substructural deformation gradients is governed by the substructural plastic velocity gradients in a manner similar to that for the continuum. Certain topics related to the numerical implementation are discussed and a simple integration scheme for the local constitutive equations is developed. To demonstrate the capabilities of the model it is implemented into a finite element code. Two numerical examples are considered: deformation of uniform plate with circular hole and the drawing of a cup. In the two examples it is assumed that initial cubic material symmetry applies to both the elastic and plastic behavior. To be specific, a polyconvex Helmholtz free energy function together with a yield function of quadratic type is adopted. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
finite strains, anisotropy, spatial form
in
International Journal of Solids and Structures
volume
44
issue
10
pages
3514 - 3532
publisher
Elsevier
external identifiers
  • wos:000246273100023
  • scopus:33947107510
ISSN
0020-7683
DOI
10.1016/j.ijsolstr.2006.10.002
language
English
LU publication?
yes
id
843c3875-0284-42bc-b84b-aa0a10dcc140 (old id 664561)
date added to LUP
2007-12-07 15:51:40
date last changed
2017-08-27 05:15:05
@article{843c3875-0284-42bc-b84b-aa0a10dcc140,
  abstract     = {A phenomenological model for evolving anisotropy at large strains is presented. The model is formulated using spatial quantities and the anisotropic properties of the material is modeled by including structural variables. Evolution of anisotropy is accounted for by introducing substructural deformation gradients which are linear maps similar to the usual deformation gradient. The evolution of the substructural deformation gradients is governed by the substructural plastic velocity gradients in a manner similar to that for the continuum. Certain topics related to the numerical implementation are discussed and a simple integration scheme for the local constitutive equations is developed. To demonstrate the capabilities of the model it is implemented into a finite element code. Two numerical examples are considered: deformation of uniform plate with circular hole and the drawing of a cup. In the two examples it is assumed that initial cubic material symmetry applies to both the elastic and plastic behavior. To be specific, a polyconvex Helmholtz free energy function together with a yield function of quadratic type is adopted.},
  author       = {Harrysson, Magnus and Harrysson, Anders and Ristinmaa, Matti},
  issn         = {0020-7683},
  keyword      = {finite strains,anisotropy,spatial form},
  language     = {eng},
  number       = {10},
  pages        = {3514--3532},
  publisher    = {Elsevier},
  series       = {International Journal of Solids and Structures},
  title        = {Spatial representation of evolving anisotropy at large strains},
  url          = {http://dx.doi.org/10.1016/j.ijsolstr.2006.10.002},
  volume       = {44},
  year         = {2007},
}