Table Of ContentADVANCED TOPICS
IN SCIENCE AND TECHNOLOGY IN CHINA
ADVANCED TOPICS
IN SCIENCE AND TECHNOLOGY IN CHINA
Zhejiang University is one of the leading universities in China. In Advanced
Topics in Science and Technology in China, Zhejiang University Press and
Springer jointly publish monographs by Chinese scholars and professors, as well
as invited authors and editors from abroad who are outstanding experts and
scholars in their fields. This series will be of interest to researchers, lecturers, and
graduate students alike.
Advanced Topics in Science and Technology in China aims to present the latest
and most cutting-edge theories, techniques, and methodologies in various research
areas in China. It covers all disciplines in the fields of natural science and
technology, including but not limited to, computer science, materials science, life
sciences, engineering, environmental sciences, mathematics, and physics.
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Mao-Hong Yu
Jian-Chun Li
Computational Plasticity
With Emphasis on the Application of the
Unified Strength Theory
With 458 figures, 139 of them in color
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Series:
1. Unified Strength Theory and Its Applications. Yu MH, Springer: Berlin,
2004.
2. Generalized Plasticity. Yu MH et al. Springer: Berlin, 2006.
3. Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses of
Structures. Yu MH, Ma GW and Li JC, Springer and ZJU Press, 2009.
4. Computational Plasticity: With Emphasis on the Application of the
Unified Strength Theory and Associated Flow Rule. Yu MH and Li JC,
Springer and ZJU Press, 2012.
Mao-Hong Yu
Jian-Chun Li
Computational Plasticity
With Emphasis on the Application of the
Unified Strength Theory
With 458 figures, 139 of them in color
Authors
Prof. Mao-Hong Yu Researcher Jian-Chun Li
Department of Civil Engineering Swiss Federal Institute of Technology
Xi’an Jiaotong University, Xi’an, China Switzerland
E-mail: [email protected] E-mail: [email protected]
ISSN 1995-6819 e-ISSN 1995-6827
Advanced Topics in Science and Technology in China
ISBN 978-7-308-08356-0
Zhejiang University Press, Hangzhou
ISBN 978-3-642-24589-3 ISBN 978-3-642-24590-9 (eBook)
Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2011938950
© Zhejiang University Press, Hangzhou and Springer-Verlag Berlin Heidelberg 2012
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Preface
Computational plasticity is a new and important branch of computational
mechanics. Computational Plasticity: With Emphasis on the Application of the
Unified Strength Theory and Associated Flow Rule is the third title in the series on
plasticity published by Springer and by Springer or by the collabration of Springer
and ZJU Press. The other two files are: Generalized Plasticity (Springer, Berlin,
2006) and Structural Plasticity: Limit, Shakedown and Dynamic Plastic Analyses
of Structures (Springer and ZJU Press, Hangzhou, 2009). The founding work in
this series on plasticity is Unified Strength Theory and its Applications that was
published by Springer in Berlin in 2004, in which the unified strength theory (UST)
and its 30 years developments history are described in detail.
Generalized Plasticity, the first monograph in this series on plasticity, is a
combination of traditional plasticity for metallic materials (non-SD materials) and
plasticity for geomaterials (SD materials, i.e. strength difference in tension and in
compression, sometimes referred to as tension-compression asymmetry). It was
published by Springer in 2006, in which the unified slip line theory for plane
strain problems and unified characteristics theory for plane stress and spatial
axisymmetric problems, as well as the unified fracture criterion for mixed mode
cracks and plastic zones at the tip of a crack using the unified strength theory are
described. Generalized Plasticity can be used for both non-SD materials and SD
materials. The time effect, however, is not taken into account in Generalized
Plasticity. The time independent UST can be extended to time dependent UST.
The second title in this series on plasticity is Structural Plasticity: Limit,
Shakedown and Dynamic Plastic Analyses of Structures, which was published by
ZJU Press and Springer in 2009. Structural Plasticity deals with limit analysis,
shakedown analysis and dynamic plastic analyses of structures using the analytical
method. The straight line segments on the series yield surfaces of the unified
strength theory make these surfaces convenient for analytical treatment of
plasticity problems. A series of results of the unified solutions for elastic and
plastic limit analysis, shakedown analysis and dynamic plastic analysis for
structures are given by using the unified strength theory. These unified solutions
can provide a very useful tool for the design of engineering structures. Most
solutions in textbooks regarding the plastic analysis of structures are special cases
of the unified solution, using the unified strength theory.
VI Preface
The third title in this series on plasticity is Computational Plasticity: With
Emphasis on the Application of the Unified Strength Theory and Associated Flow
Rule, in which numerical methods are applied. The unified strength theory and
associated flow rule are implemented in several computational plasticity codes and
applied to many engineering problems.
A series of results can be obtained in Generalized Plasticity (slip line theory),
Structural Plasticity (analytical analysis of structures) and Computational
Plasticity (numerical analysis of structures). The unified solution gives a series of
new results, which can be adapted for more materials and structures. It is possible
for us to adopt different values of the unified strength theory parameter b to meet
different materials and structures. The application of the unified solution is
advantageous in material and energy saving and also advantageous in
environmental protection.
This monograph describes the unified strength theory and associated flow rule,
the implementation of these basic theories, and shows how a series of results can
be obtained by their use. A lot of numerical solutions for beams, plates,
underground caves, excavations, strip foundations, circular foundations, slopes,
underground structures of hydraulic power stations, pumped-storage power
stations, underground mining, high-velocity penetration of concrete structures,
ancient structures, rocket parts, as well as relevant computational results, are given.
These theories and methods can be used for other computer codes. This will
increase the function of codes. An example of numerical calculation for a slope by
using the unified strength theory with the parameters b=0, b=1/4, b=0.5, b=3/4 and
b=1 is shown in the figure below. Configurations of the plastic strain of the slope
with different yield criteria are shown. The results using the Mohr-Coulomb
theory and the Drucker-Prager criterion are also given for comparison.
Mohr-Coulomb
b=0.0
b=0.25
Drucker-Prager
b=0.5
b=0.75
b=1.0
Preface VII
The results obtained by using various yield criteria are very different. The
shape and size of the plastic zone and bearing capacity of the structure are
influenced strongly by the choice of the yield criterion. The unified strength theory
and its implementation in the computer code provide us with a very effective
approach for studying the effect of yield criterion in various engineering problems.
A series of results was obtained, which can be used for most materials from
metallic materials to geomaterials. The unified model, unified constitutive relation,
unified process of the corner singularity, and the program paragraph of unified
implementation can be used for other FE codes, including commercial computer
codes. This will also increase the power of FEM and computational plasticity
codes and the fields of application for various codes.
Many new and interesting results can be obtained through the unified strength
theory, such as the yield criterion effect on the bearing capacity of various
structures, the effect of material strength parameters (friction angle) on plastic
zones distribution (Chapter 9), the effect of tension and compression of SD
materials, the relation between different yield criteria. This will bring the potential
strength of the material into full play and show how we can benefit from material
and energy saving, etc.
The contents of this book can be divided into four parts:
Part one: Basic theories of stress, strain, yield criterion and associated flow
rule are described in Chapters 1 to 4.
Part two: Implementation of the unified strength theory and associated flow rule,
the process of the singularity of the corner and several basic applications,
UEPP-Unified Elasto-Plastic Program, are described in Chapters 5 to 9.
Part three: Chapters 10 to 18 are the implementation of the unified strength
theory and associated flow rule in several commercial finite element codes and finite
difference programs, including ABAQUS, ASYSN, AutDYN-2D, AutDYN-3D,
AutDYN Hydrocode, DIANA, FLAC-2D, FLACK-3D, Non-Linear etc. The
computational methods include the finite element method, finite difference method
and smoothed particle hydrodynamics (SPH) method. More results can be obtained
through combinations of the unified strength theory and associated flow rule and
commercial finite element codes
Part four: Chapter 19 is called Mesomechanics and Multiscale Modelling for
the Yield Surface. Miscellaneous issues, including ancient structures, propellant
grains of solid rockets, solid rocket motors, parts of a rocket and large generators
are presented in Chapter 20.
A series of research works of underground excavation were carried out for the
Laxiwa Hydraulic Power Station by Northwest China Hydroelectric Power
Investigation and Design Institute. 3D numerical modeling of the underground
excavation of Tai’an Pumped Storage Hydraulic Power Station was done by
Professors Sun, Shang, Zhang et al. of Zhejiang University, Hangzhou, China and
the East China Investigation and Design Institute, State Power Corporation of
China. Dynamic response and blast-resistance analysis of a tunnel subjected to
blast loading was done by Professors at Zhejiang University, Hangzhou(cid:712)China, in
respect of a railroad tunnel (Liu and Wang, 2004). The twin-shear unified strength
