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### FE-formulation of a nonlocal plasticity theory

and Ristinmaa, Matti LU (1996) In Computer Methods in Applied Mechanics and Engineering 136(1-2). p.127-144
Abstract
A nonlocal continuum plasticity theory is presented. The nonlocal field introduced here is defined as a certain weighted average of the corresponding local field, taken over all the material points in the body. Hereby, a quantity with the dimension of length occurs as a material parameter. When this so-called internal length is equal to zero, the local classical plasticity theory is regained. In the present model, the yield function will depend on a nonlocal field. The consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers. The integral equations are classified as Fredholm equations of the second kind and the existence of a solution will be commented upon.... (More)
A nonlocal continuum plasticity theory is presented. The nonlocal field introduced here is defined as a certain weighted average of the corresponding local field, taken over all the material points in the body. Hereby, a quantity with the dimension of length occurs as a material parameter. When this so-called internal length is equal to zero, the local classical plasticity theory is regained. In the present model, the yield function will depend on a nonlocal field. The consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers. The integral equations are classified as Fredholm equations of the second kind and the existence of a solution will be commented upon. After discretization, a matrix equation is obtained, and an algorithm for finding the solution is proposed. For a generalized von Mises material, a plane boundary value problem is solved with a FE-method. Since the nonlocal quantities are integrals, C0-continuous elements are sufficient. The solution strategy is split into a displacement estimate for equilibrium and the integration of constitutive equations. In the numerical simulations shear band formation is analysed and the results display mesh insensitivity. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Finite element, nonlocal plasticity
in
Computer Methods in Applied Mechanics and Engineering
volume
136
issue
1-2
pages
127 - 144
publisher
Elsevier
external identifiers
• scopus:0030247714
ISSN
0045-7825
DOI
10.1016/0045-7825(96)00997-8
language
English
LU publication?
yes
id
c5adca8f-96a2-4ec5-b862-8ea490629153 (old id 2223688)
date added to LUP
2011-12-06 13:24:04
date last changed
2019-02-20 09:40:11
```@article{c5adca8f-96a2-4ec5-b862-8ea490629153,
abstract     = {A nonlocal continuum plasticity theory is presented. The nonlocal field introduced here is defined as a certain weighted average of the corresponding local field, taken over all the material points in the body. Hereby, a quantity with the dimension of length occurs as a material parameter. When this so-called internal length is equal to zero, the local classical plasticity theory is regained. In the present model, the yield function will depend on a nonlocal field. The consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers. The integral equations are classified as Fredholm equations of the second kind and the existence of a solution will be commented upon. After discretization, a matrix equation is obtained, and an algorithm for finding the solution is proposed. For a generalized von Mises material, a plane boundary value problem is solved with a FE-method. Since the nonlocal quantities are integrals, C0-continuous elements are sufficient. The solution strategy is split into a displacement estimate for equilibrium and the integration of constitutive equations. In the numerical simulations shear band formation is analysed and the results display mesh insensitivity.},
author       = {Strömberg, Lena and Ristinmaa, Matti},
issn         = {0045-7825},
keyword      = {Finite element,nonlocal plasticity},
language     = {eng},
number       = {1-2},
pages        = {127--144},
publisher    = {Elsevier},
series       = {Computer Methods in Applied Mechanics and Engineering},
title        = {FE-formulation of a nonlocal plasticity theory},
url          = {http://dx.doi.org/10.1016/0045-7825(96)00997-8},
volume       = {136},
year         = {1996},
}

```