A study of plasticity by gruops on pseudo-Euclidean spaces and experiments (1/3)
Date Issued
2000
Date
2000
Author(s)
DOI
892211E002032
Abstract
The project employed a group-theoretical ap-
proach to investigate constitutive models of
elastoplasticity. In the axial-torsional test, the
hoop and radial strains are usually not known a
priori; hence, in the constitutive model simula-
tion of the responses they can not be viewed as
inputs. This greatly complicates the constitutive
analyses because the resulting differential con-
stitutive equations become highly nonlinear. To
tackle this diffculty we convert the highly nonlin-
ear axial-torsional problem of perfect elastoplas-
ticity to a quasi-linear system _X = A(X; t)X,
where A(X; t) 2 sl(2; 1;R) is a local Lie algebra
of the special pseudo-linear group SL(2; 1;R).
The underlying space of this problem is found
to be a pseudo-Riemann manifold which is lo-
cally pseudo-Euclidean space E3
2;1 with the metric
indefinite and also dependent on the time com-
ponent. Utilizing the internal symmetry group,
we can consequently develop a highly accurate
group-preserving scheme, which guarantees the
fulfillment of the consistency condition in every
time marching of the calculations.
The axial-torsional test equipment MTS809 of
the NTU College of Engineering and the pressure
control machine was used to study the cyclic and
ratchetting behavior of tubular specimens of Al-
7075 and stainless steel 316.
We also studied contraction ratios experimen-
tally, one rate form and one total form under dif-
ferent initial values of the specimens. The values
of both contraction ratios may be greater than
1=2. Moreover, for some cases we found that the
rate form contraction ratio exceeds the value 1.
Subjects
plasticity
pseudo-Riemann manifold
special pseudo-linear group
axial-torsional cyclic test
contraction ratio
Publisher
臺北市：國立臺灣大學土木工程學系暨研究所
Type
report
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