Kounadis A.N., Gdoutos E.E. (Eds.) Recent Advances in Mechanics

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X Preface

“An Asymptotic Method of Boundary-Value Problems Solution of Elasticity

Theory for Thin Bodies,” by L.A. Aghalovyan discusses an asymptotic method for

the solution of the first, second and mixed boundary value problems of elasticity

theory for layered beams, plates and shells. The method permits the solution of

dynamic problems of thin bodies. General asymptotic solutions are obtained.

“Reliable Optimal Design in Contact Mechanics,” by N.V. Banichuk, S. Yu.

Ivanova and E.V. Makeev formulates the problem of contact pressure optimiza-

tion for the case of a rigid punch interacted with an elastic medium. The shape of

the punch is considered as an unknown design variable. The total forces and mo-

ments applied to the punch and the loads acted at the outside regions are given.

Optimal shapes are found analytically for punches having rectangular contact

domains.

“Scaling of Strength and Lifetime Distributions of Quasibrittle Structures,” by

Z.P. Bažant and J.-L. Le presents a refined theory on the strength distribution of

quasibrittle structures, which is based on the fracture mechanics of nanocracks

propagating by activation energy controlled small jumps through a nano-structure

and an analytical model for the multi-scale transition of strength statistics. It

is shown that the theory matches the experimentally observed systematic devia-

tions of strength and lifetime histograms of industrial ceramics from the Weibull

distribution.

“Directional Distortional Hardening in Plasticity within Thermodynamics,” by

Y.F. Dafalias and H.P. Feigenbaum presents a complete theory for metal plasticity

that includes directional distortional hardening supplemented by the classical

kinematic and isotropic hardenings. It is shown that the theory fits well experi-

mentally found yield surfaces and can be used to simulate stress controlled biaxial

ratcheting with good accuracy.

“Forced Vibrations of the System: Structure – Viscoelastic Layer,” by B.V.

Gusev and A. S. Faivusovich presents analytical solutions of the problem of inter-

related vibrations of an elastic structure with viscoelastic layer. The investigations

were made to work out the method of the dynamical computation and optimiza-

tion of technological processes for forming reinforced concrete articles on the

shock and vibration machines and shock machines developed by the authors were

used. Numerical results and experimental data were presented.

“Extreme Instability Phenomena in Autonomous Weakly Damped Systems:

Hopf Bifurcations, Double Pure Imaginary Eigenvalues, Load Discontinuity,” by

A.N. Kounadis reconsiders the dynamic asymptotic instability of autonomous

multi-parameter discrete systems under step compressive loading (conservative or

nonconservative) using the efficient - and rather forgotten - Lienard-Chipart sta-

bility criterion. Attention is focused on the interaction of nonuniform mass distri-

bution and infinitesimal damping which may have a tremendous effect on the

Jacobian eigenvalues and thereafter on the local asymptotic instability.

“Variational Approach to Static and Dynamic Elasticity Problems,” by G.G.

Kostin and V.V. Saurin considers the integrodifferential approach incorporated in

the variational technique for linear elastic static and dynamic problems. A family

of static and dynamical variational principles, in which displacement, stress,

and momentum fields are varied, is proposed. A regular numerical algorithm of

Preface XI

constrained minimization for the initial-boundary value problem is developed. The

case of an optimization problem of lateral controlled motions of a 3D rectilinear

elastic prism with a rectangular cross section is investigated.

“An Accelerated Newmark Scheme for Integrating the Equation of Motion of

Nonlinear Systems Comprising Restoring Elements Governed by Fractional De-

rivatives,” by G.I. Evangelatos and Pol. D. Spanos develops a new algorithm for

numerical integration of the equations of motion of a nonlinear system with damp-

ing governed by fractional derivatives in the time domain. The major advantage of

this approach is that, a very small number of past terms are required and, the calcu-

lation of the effective values of mass damping and stiffness is performed only once.

Experimental Mechanics

“Photoelastic Tomography as Hybrid Mechanics,” by H. Aben, L. Ainola, and A.

Errapart develops a non-destructive method based on the use of equations of the

theory of elasticity and hybrid algorithms for the determination of axisymmetric

stress fields in arbitrary sections of test objects. The method is used for the deter-

mination of residual stresses in glass.

“Using an Electronic Speckle Interferometry for Measurement of a Stress-

Deformation State of Elastic Bodies and Structures,” by R.V. Goldstein, V.M.

Kozintsev and A.L. Popov presents the method and related equipment of the elec-

tronic speckle pattern interferometry (ESPI) for studying stress and deformation

fields in elastic bodies and structures. ESPI is used for measurement of residual

stresses in welded structures, micro-displacements related to delamination of thin

coatings, diagnostics of shrinkage stresses in coatings and determination of their

elastic characteristics. The method is generalized for measuring displacements at

the nanometer scale.

“Structural Integrity and Residual Strength of Composites Exposed to Fire,”

by G.A. Kardomateas studies the compressive response of an axially restrained

composite column, which is exposed to a heat flux due to fire by analytical and

experimental means. The column is exposed to fire from one-side and an analyti-

cal approach is outlined for the resulting heat damage, the charred layer formation

and non-uniform transient temperature distribution. Due to the nonuniform stiff-

ness and the effect of the ensuing thermal moment, the structure behaves like an

imperfect column, and responds by bending rather than buckling in the classical

Euler (bifurcation) sense.

“Theory and Application of Sampling Moiré Method.” by Y. Morimoto and

M. Fujigaki introduces the theory of sampling moiré and uses it for the measure-

ment of the displacements of a beam and the shape and strains of a rubber struc-

ture. The method uses an image processor of a grating pattern on an object

recorded by a digital camera. It has the advantage of non-contact measurement of

displacements with simplicity, high accuracy, high speed, and low cost. The

method can easily be applied to dynamic problems with a high-speed camera.

“Recent Advances in Microelectromechanical Systems and their Applications

for Future Challenges,” by R.J. Pryputniewicz presents recent advances in opto-

electronic methodology for micro- and nano-scale measurements and their use is

XII Preface

illustrated with representative examples of microelectromechanical systems

(MEMS) operating at high frequencies and used in demanding environments. Ad-

vances in emerging technologies of MEMS and nanotechnology, especially relat-

ing to the applications, constitute one of the most challenging tasks in today’s

micromechanics and nanomechanics. Development of miniscule devices requires

sophisticated design, analysis, fabrication, testing, and characterization tools and

should be based on a combined use of the analytical, computational, and experi-

mental solutions methodology.

“Experimental Mechanics in Nano-Engineering,” by C.A. Sciammarella,

F.M. Sciammarella and L. Lamberti presents a new approach to studies at the

nano-scale based on the use of evanescent illumination. The proposed methodol-

ogy provides the means of measuring the dimensions and shapes of objects,

surface topography, roughness and strains allowing the precise detection of infor-

mation at the nano-scale. It is shown that evanescent illumination is the key to

making experimental mechanics methodologies well suitable for nano-engineering

applications. Nanometer resolutions were achieved by using experimental setups

that included a conventional optical microscope.

“Advanced Cement Based Nanocomposites,” by S.P. Shah, M.S. Konsta-

Gdoutos and Z.S. Metaxa studies the development of high-performance cementi-

tious nanocomposites reinforced with multiwall carbon nanotubes (CNTs). Effective

dispersion was achieved by applying ultrasonic energy and with the use of a surfac-

tant. Fracture mechanics test results indicate that the fracture properties of cement

matrix increased through proper dispersion of small amounts of CNTs (0.025wt%

and 0.08wt%). Nanoindentation results suggest that CNTs can modify and reinforce

the cement paste matrix at the nanoscale by increasing the amount of high stiffness

C-S-H and decreasing the porosity, which leads to the reduction of the autogenous

shrinkage.

“Application of Digital Speckle Pattern Interferometry (DSPI) in Determina-

tion of Elastic Modulus Using Plate Vibration,” by Ch. Shakher and R. Kumar

presents a technique for the evaluation of the elastic modulus of materials based

on the vibration analysis of a plate using digital speckle pattern interferometry and

the Rayleigh method. A series of experiments were conducted on square alumin-

ium plates with one edge fixed and other edges free. The experimental results

show that a single observation of frequency at first torsional mode is sufficient to

determine the elastic modulus for all practical purposes.

“The Development and Applications of Amplitude Fluctuation Electronic

Speckle Pattern Interferometry Method,” by W.-C. Wang and C.-H. Hwang pre-

sents the development and improvement of an amplitude fluctuation electronic

speckle pattern interferometry (ESPI) method. The effects of environmental noise

and vibration characteristics on the ESPI fringe pattern are investigated. Theoreti-

cal derivation of the effect of environmental noise is performed and the time vary-

ing brightness of the traditional time averaged (TA) ESPI fringe patterns is

successfully explained. Furthermore, applications of the method are briefly

reviewed.

Preface XIII

Fracture Mechanics

“Piezonuclear Transmutations in Brittle Rocks under Mechanical Loading:

Microchemical Analysis and Geological Confirmations,” by A. Carpinteri,

G. Lacidogna, A. Manuello and O. Borla reports Neutron emission measurements

by means of

He devices and neutron bubble detectors during three different kinds

of compression tests on brittle rocks: (i) under displacement control, (ii) under

cyclic loading, and (iii) by ultrasonic vibration. It is shown that piezonuclear reac-

tions giving rise to neutron emissions are possible in inert non-radioactive solids

under loading.

“Stress Triaxiality at Crack Tips Studied by Caustics,” by E.E. Gdoutos studies

the three-dimensional nature of the stress field in the vicinity of the crack tip. It

also analyzes the conditions that should be satisfied among the dimensions of the

optical arrangement and the specimen properties and thickness in order the caustic

to be generated by the light rays transmitted or reflected from the region of the

specimen where plane stress conditions dominate.

“Reinforcement of a Cracked Infinite Elastic Plate with Defects,” by S.M.

Mkhitaryan and D.I. Bardzokas studies a series of linear elastic crack problems

with reinforcements, that are classified as contact problems, and are treated by

using complex analysis and singular integral equations. The optimal position of

the reinforcement can be selected in order to obtain lower stress intensity factors

at the crack tips.

“Some Actual Problems of Fracture Mechanics of Materials and Structures,”

by V.V. Panasyuk and I.M. Dmytrakh presents some theoretical and experimental

results on problems of fracture mechanics of materials and on durability of struc-

tural elements. Conceptual problems of fracture mechanics and strength of

cracked materials are formulated. Furthermore, actual problems of fracture me-

chanics and strength of materials in service environments are considered.

“Cyclic Plasticity with an Application to Extremely Low Cycle Fatigue of

Structural Steel,” by D. Sumarac and Z. Petraškoviü shows that the Preisach

model has several advantages when it is applied to the problem of so called cyclic

stable plasticity of axially loaded members. The model is applied to extremely low

fatigue. This case is very important for design of dampers applied for reconstruc-

tion of seismically damaged structures, because the Manson-Coffin Law overes-

timates the number of cycles before failure.

“The Fracture Toughness of a Highly Filled Polymer Composite,” by O.A.

Stapountzi, M.N. Charalambides and J.G. Williams reports fracture toughness

values for an ATH-PMMA composite for filler volume fractions ranging from

0.35 to 0.49 and tested over the temperature range from 0 to 90 °C. It is obtained

that the toughness decreases with increasing filler content contrary to expecta-

tions. Using a toughness model it was possible to calculate the adhesion energy of

the particles and the average particle size.

It is with profound sorrow to announce the unexpected death of one of the

authors of the book Professor Dimos Bartzokas. Dimos was a colleague at

the National Technical University of Athens, and a good friend. May his memory

be eternal.

XIV Preface

We would like to thank the authors who accepted the editors’ invitation to par-

ticipate in the symposium and to contribute to this book. Thanks are also due to

the Academy of Athens, the National Technical University of Athens, the Pericles

S. Theocaris Foundation and Ms Eugenia Theocaris who sponsored this sympo-

sium. A special word of thanks goes to Mrs. Nathalie Jacobs of Springer for her

kind and continuous collaboration and support and the esthetic appearance of this

book.

With humble respect to the memory of the late Professor and Academician

P.S. Theocaris, we present this book to the mechanics community as a small trib-

ute to his service, leadership and contributions to the mechanics community.

September 2010 A.N. Kounadis

E.E. Gdoutos

Pericles S. Theocaris

Biography

Pericles S. Theocaris

Professor - Academician

P.S. Theocaris was descendant of a noble family from the heroic town of

Kalavryta of the prefecture of Patras, Greece, son of the army General Stavros

Theocaris. He was born in Athens on September 24, 1921. He registered in the

Hellenic Military Academy of Athens in 1938. As a junior student he participated

in the Greek-Italian war of 1940 and served for six months in the Albanian front.

For his heroic acts during the war he was decorated with the Golden Medal of

Bravery.

In 1942 he registered at the National Technical University of Athens (NTUA)

and graduated in 1948 with the Diploma of Mechanical-Electrical engineer, first in

his class with the highest degree among all classes of all Schools of NTUA. During

his studies he was awarded five prizes. From January 1949 to April 1951 he served

in the Army as a captain of the Technical Corps.

In 1951 he obtained a fellowship for specialized studies at M.I.T. (U.S.A.) for six

months. He was awarded a scholarship by the University of Brussels and a scholarship

the French government for postgraduate studies. He obtained: a) the degree of Doctor

of Applied Sciences, with Great Distinction from the University of Brussels in

March 1953, and b) in November 1953 the degree of Doctor of Physical Sciences

from the University of Paris with very honorable mention.

In September 1957 he obtained a fellowship at the National Academy of Sci-

ences and National Research Council of the U.S.A. and he was appointed Visiting

Research Fellow at the Illinois Institute of Technology, in Chicago. In 1958 he was

appointed Visiting Assistant Professor at Brown University, U.S.A.

In 1960 he was elected Professor and Director of the Laboratory for Testing Mate-

rials (LTM) at the Athens National Technical University. During his directorship

LTM was classified as one of the best laboratories of testing materials worldwide. He

was invited by the French government to be Research Visitor at the Central Labo-

ratory of Bridges and Roads of the Ministry of Public Works of France. In 1963 he

was appointed Visiting Professor at the Department of Mechanics of Pennsylvania

State University, U.S.A. In October 1965 he was a Research Visitor at the Ernst

Mach Institute of the University of Freiburg, Germany.

In 1968 he was elected Professor (Full) at the Chair of Theoretical and Applied

Mechanics of NTUA. In 1969 he served as Member of the Senate of NTUA. He

was elected Rector of the National technical University of Athens twice in 1974

and in 1979 and contributed to the foundation of the Technical University of Crete

XVIII Biography

as President of the Board of Trustees (1974 - 1979). In 1980 he was honored with

the title of “Rector Magnificus” of the National Technical University of Athens.

• In 1973 he was elected member of the National Academy of Athens

(Section of Sciences).

• In 1983 he was elected President of the Academy of Athens and during

the period 1989-1994 Secretary General.

• In 1974 he was appointed Vice-Minister of National Education in the

caretaker government of Greece and Vice-President of the board of

Trustees of the National Observatory of Athens.

• From 1989 to 1991 he was appointed Secretary General in the General

Secretariat of Research and Development.

• In September 1978, he served as President of the Greek Council for the

Exhibition of Greek Antiquities in Paris, New York and Moscow under

the title: Greek Art of the Aegean Islands (1979).

• From 1980 to 1987 he served as Scientific Greek Representative to the

International Council of Scientific Unions (ICSU).

• In October 1982 he was elected fellow of the Archeological Society of

Athens.

• From 1978 until 1995 he was President of the Hellenic Society of

Theoretical and Applied Mechanics.

• He was member of the following National Academies: Royal Academy

of Engineering of Great Britain, Serbian Academy of Sciences and

Arts, Bulgarian Academy of Sciences, Academia Tiberina of Italy,

International Academy of Sciences of Germany and of Academia

Europea of which he was a founding member. In March 1991 he was

elected member of Academia Scientiarum et Artium Europaea.

• He was member of many scientific councils and was awarded with the

following prizes: Empeirikeion Prize, 1971 (President of the

Empeirikeion Foundation in 1974), Bernard Hall Prize of Great Britain

(1974), Aurel Vlaicou Prize of Romania (1980)

• In 1996 the Aristotelean University of Thessaloniki and in 1999 the

Democritus University of Thrace granted him the degree of Doctor of

Science honoris causa.

He received the following military medals:

 Golden Medal of Bravery

 Silver Cross with Swords of the Order of King George A

 Military Cross

 Medal of Extraordinary Actions

 Medal of the Greek-Italian war

For his scientific activities, his contribution to the advancement of the science

of Mechanics he was awarded the following medals:

 Golden Cross of the Order of King George A

 Commander of the Order of Phoenix

Biography XIX

 Commander of the Order of Valour

 Grand Cross of Merit of the Patriarchate of Alexandria and all

Africa

 Notable Castrinsius of the Holy See of the Patriarchate of

Canstantinople

 Finally, in July 8, 1999 the President of the Hellenic Republic

bestowed him the Great Brigade of the Order of Merit

His scientific work includes 948 papers and books. During the years 1988-1997

he was the author with the greatest number of published papers in Applied Me-

chanics, according to the journal of Applied Mechanics Reviews.

P.S. Theocaris, in addition to his above-mentioned scientific work in Mechan-

ics and Applied Mathematics, published exceptional articles for the history of Hel-

lenic Science from Homeric to Byzantine era as well as studies of purely historic

nature, in general.

He started his life as a hero of the Greek-Italian war in the Albanian front,

continued with an outstanding academic career to become finally adorer of the

Hellenic Ideal, to a true hierophant of science, and a distinguished leader of the

modern Hellenism.

P.S. Theocaris passed away on September 14, 1999.

Research Activities

General Description

Professor P.S. Theocaris published 948 books and papers. They may be grouped in

the following nine main categories:

(1) One hundred and sixty papers, which deal with problems of elastic-

ity and plasticity by optical methods. New theoretical methods based on the

theory of complex variables and the properties of isostatics were introduced by

P.S. Theocaris. The experimental solution of elastic-plastic problems by using the

experimental methods of photoelastic coatings, moiré and the electrical analogies

were advanced for the first time. The photoelastic method (classical and photoelastic

coatings) was extended in different problems of the praxis and important applica-

tions were introduced. The matrix theory based on the Muller and Jones calculus and

the Poincaré sphere were developed. These developments were included in an au-

thoritative book published by Springer-Verlag. Closed-form solutions for solving

systems of higher order differential equations and closed-form solutions to difficult

problems of complicated shell-, beam- and frame-structures in civil engineering

were introduced in an elegant manner.

(2) He developed the experimental method of moiré for evaluating dis-

placement and strain fields. Seventy one papers deal exclusively with the method.

He authored the first book on moiré fringes entitled “Moiré Fringes in Strain Analy-

sis”, published by Pergamon Press in 1969.

(3) Viscoelasticity and rheology of high polymers, also including the

mesophase model was another area of his scientific activities. Ninety seven

papers deal exclusively with this subject. P.S. Theocaris extended the