An elastic-perfectly plastic flow model for finite element analysis of perforated materials Page: 4 of 11
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An Elastic-Perfectly Plastic Flow Model for Finite
Element Analysis of Perforated Materials
D. P. Jones*, J. L. Gordon*, D. N. Hutula, D. Banas, J. B. Newman
Bechtel Bettis, Inc.
Bettis Atomic Power Laboratory
West Mifflin, Pennsylvania
This paper describes the formulation of an
elastic-perfectly plastic flow theory
applicable to equivalent solid [EQS]
modeling of perforated materials. An
equilateral triangular array of circular
penetrations is considered. The usual
assumptions regarding geometry and
loading conditions applicable to the
development of elastic constants for EQS
modeling of perforated plates are
considered to apply here. An elastic-
perfectly plastic [EPP] EQS model is
developed for a collapse surface that
includes fourth-order stress terms. The
fourth order yield function has been shown
to be appropriate for plates with a triangular
array of circular holes. A complete flow
model is formulated using the consistent
tangent modulus approach based on the
fourth order yield function.
EQS-EPP method is used to obtain a limit
load solution for a plate subjected to
transverse pressure and fixed at the outer
edge. This solution is compared to a
solution obtained with an EPP-FEA model in
which each penetration in the plate is
modeled explicitly. The calculated limit load
from using the EQS-EPP model is 8% lower
than the limit load calculated by the explicit
Pitch of pattern, mm
Diameter of penetrations, mm
Minimum ligament width, (P-d),
p. Ligament efficiency, h/P
(Ti, E; Stress and strain vectors for i = xx,
yy, zz, xy, zx, yz components,
MPa and mm/mm
EQS Equivalent solid
Sy Yield stress of material, MPa
So= Sy Effective yield stress of EQS
D Elastic matrix, MPa
T Tangent modulus matrix, MPa
Superscripts E and p refer to elastic and
plastic components. Bold type is used to
distinguish vectors and matrix quantities.
Elastic analysis procedures are well
developed for the equivalent solid [EQS]
treatment of perforated materials. These
methods have proven to be very useful in
the analysis of perforated plates found in
pressure vessel applications such as tubular
Extension of EQS elastic methods to
elastic-perfectly plastic [EPP] material
response has not progressed as far owing
in part to complex nature of the yield
surfaces needed to describe yielding of
perforated materials and to a sense that
elastic methods are sufficient for design of
Incentive for further development of EPP-
EQS solution capability for perforated plates
has recently increased as improvements in
computer capabilities have made
contemplation of EPP finite element
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Jones, D.P.; Gordon, J.L.; Hutula, D.N.; Banas, D. & Newman, J.B. An elastic-perfectly plastic flow model for finite element analysis of perforated materials, article, February 1, 1999; West Mifflin, Pennsylvania. (https://digital.library.unt.edu/ark:/67531/metadc704651/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.