FEformulation of a nonlocal plasticity theory
(1996) In Computer Methods in Applied Mechanics and Engineering 136(12). p.127144 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 socalled 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 socalled 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 FEmethod. Since the nonlocal quantities are integrals, C0continuous 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:
http://lup.lub.lu.se/record/2223688
 author
 Strömberg, Lena and Ristinmaa, Matti ^{LU}
 organization
 publishing date
 1996
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Finite element, nonlocal plasticity
 in
 Computer Methods in Applied Mechanics and Engineering
 volume
 136
 issue
 12
 pages
 127  144
 publisher
 Elsevier
 external identifiers

 scopus:0030247714
 ISSN
 00457825
 DOI
 10.1016/00457825(96)009978
 language
 English
 LU publication?
 yes
 id
 c5adca8f96a24ec5b8628ea490629153 (old id 2223688)
 date added to LUP
 20111206 13:24:04
 date last changed
 20180107 11:04:35
@article{c5adca8f96a24ec5b8628ea490629153, 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 socalled 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 FEmethod. Since the nonlocal quantities are integrals, C0continuous 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 = {00457825}, keyword = {Finite element,nonlocal plasticity}, language = {eng}, number = {12}, pages = {127144}, publisher = {Elsevier}, series = {Computer Methods in Applied Mechanics and Engineering}, title = {FEformulation of a nonlocal plasticity theory}, url = {http://dx.doi.org/10.1016/00457825(96)009978}, volume = {136}, year = {1996}, }