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Discontinuos Displacement Apprixamation for capturing Plastic Loacalization

Larsson, Ragnar; Runesson, Kenneth and Ottosen, Niels Saabye LU (1993) In International Journal for Numerical Methods in Engineering 36(12). p.2087-2105
Abstract
It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional... (More)
It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal for Numerical Methods in Engineering
volume
36
issue
12
pages
2087 - 2105
publisher
John Wiley & Sons
external identifiers
  • Scopus:0027607488
ISSN
1097-0207
DOI
10.1002/nme.1620361209
language
English
LU publication?
yes
id
5da6d49d-6bb9-4edf-a4b9-182ecbb56233 (old id 930567)
date added to LUP
2010-09-18 11:31:11
date last changed
2016-10-13 04:56:28
@misc{5da6d49d-6bb9-4edf-a4b9-182ecbb56233,
  abstract     = {It is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries (interfaces) of the finite element subdivision. The regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept. As a by-product of the regularization, an intrinsic band width is introduced as a ‘constitutive’ property rather than a geometric feature of the finite element mesh. In this way the spurious mesh sensitivity, which is obtained when the displacement approximation is continuous, can be avoided. Another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material. An interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface (up to within a scalar factor). An analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a ‘shear’ band for a general plasticity model. The significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress. It is shown that a unique structural post-peak response (in accordance with non-linear fracture mechanics) can be achieved when the plastic softening modulus is properly related to the bandwidth. The paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope.},
  author       = {Larsson, Ragnar and Runesson, Kenneth and Ottosen, Niels Saabye},
  issn         = {1097-0207},
  language     = {eng},
  number       = {12},
  pages        = {2087--2105},
  publisher    = {ARRAY(0xa1f9d98)},
  series       = {International Journal for Numerical Methods in Engineering},
  title        = {Discontinuos Displacement Apprixamation for capturing Plastic Loacalization},
  url          = {http://dx.doi.org/10.1002/nme.1620361209},
  volume       = {36},
  year         = {1993},
}