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Foundations of Elastoplasticity: Subloading Surface Model (Paperback, Softcover reprint of the original 3rd ed. 2017)
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Foundations of Elastoplasticity: Subloading Surface Model (Paperback, Softcover reprint of the original 3rd ed. 2017)
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This book is the standard text book of elastoplasticity in which
the elastoplasticity theory is comprehensively described from the
conventional theory for the monotonic loading to the unconventional
theory for the cyclic loading behavior. Explanations of
vector-tensor analysis and continuum mechanics are provided first
as a foundation for elastoplasticity theory, covering various
strain and stress measures and their rates with their
objectivities. Elastoplasticity has been highly developed by the
creation and formulation of the subloading surface model which is
the unified fundamental law for irreversible mechanical phenomena
in solids. The assumption that the interior of the yield surface is
an elastic domain is excluded in order to describe the plastic
strain rate due to the rate of stress inside the yield surface in
this model aiming at the prediction of cyclic loading behavior,
although the yield surface enclosing the elastic domain is assumed
in all the elastoplastic models other than the subloading surface
model. Then, the plastic strain rate develops continuously as the
stress approaches the yield surface, providing the advantages: 1)
The tangent modulus changes continuously, 2) The yield judgment
whether the stress reaches the yield surface is not required, 3)
The stress is automatically attracted to the yield surface even
when it goes out from the yield surface by large loading increments
in numerical calculation and 4) The finite strain theory based on
the multiplicative decomposition of deformation gradient tensor is
formulated exactly. Consequently, the monotonic, the cyclic, the
non-proportional loading behaviors for wide classes of materials
including soils, rocks and concretes in addition to metals can be
described rigorously by the subloading surface model. Further, the
viscoplastic constitutive equations in a general rate from the
quasi-static to the impact loadings are described, and constitutive
equations of friction behavior and its application to the
prediction of stick-slip phenomena, etc. are also described in
detail. In addition, the return-mapping algorithm, the consistent
tangent modulus, etc. are explained for the numerical analyses.
Further, the damage, the phase-transformation and the crystal
plasticity models are also described in brief. All of them are
based on the subloading surface model. The elastoplasticity
analysis will be advanced steadily based on the subloading surface
model.
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