彈塑性之閔氏時空群論與模式識別實驗
Date Issued
1998
Date
1998
Author(s)
DOI
872211E002035
Abstract
The project employed a group-theoretical approach to investigate
constitutive models of elastoplasticity. In a series of researches [2-6], we
have been viewing the evolution of mechanical
properties of a solid material as a differential dynamic system with
an on-off switch for plasticity mechanism, examining phenomenological
characteristics of behavior of the system subjected to
external loading. Continuing this line of thought, the project [1]
investigated theoretically the mechanical behavior from the viewpoint of
dynamic systems induced by group actions on Minkowski spacetime,
and experimentally studied a few related topics of cyclic plasticity of solid
materials, in particular the aluminum alloy Al-6061.
The emphases were placed on the global analyses of
internal symmetries in the constitutive models.
The models analyzed are perfect elastoplasticity, bilinear elastoplasticity,
isotropic-hardening,
mixed-hardening, and kinematic hardening with two intrinsic times.
It is amazing that the inclusion of action groups on
Minkowski spacetime in the frame of
dynamic systems of plasticity is very natural. With the new
concept of ``space' and ``time' in plasticity a core
connection between the causality in Minkowski spacetime, the time arrow
direction and the irreversibility of plasticity was built up.
Internal symmetry groups classify
the models of elastoplasticity and simultaneously fulfill the requirement
of causality. The groups under study included Lorentz group,
Poincar$\acute{\mbox{e}}$ group, causal group, and conformal
group.
We further developed a generalized Hamiltonian dynamic-system-theoretic
technique to construct elastoplastic models. Generalized
Hamiltonians of constitutive models were formulated through brackets,
for example, a perfect elastoplastic model through the Lie-Poisson bracket
and a non-normality flow model through the Poisson bracket.
It is found that the yield function just plays a role of the
Hamiltonian function, and the plastic potential can be used to determine
the non-canonical metric.
The axial-torsional test equipment MTS809 of the NTU College of Engineering
was used to study the cyclic and ratchetting behavior of solid bar and
tubular specimens of Al-6061. The ratchetting effect was observed in
various loading conditions, in particular, in hoop strain under cyclic
axial-torsional loading[1].
Subjects
Plasticity
differential dynamic system
Minkowski spacetime
Lorentz group
Poincar$\acute{\mbox{e}}$ group
causal group
conformal group
generalized Hamiltonian system
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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