Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'Theuseoflasersinmaterialsprocessinghasbecomewidespreadinrecent years,sothatanunderstandingofthenatureofheatandmasstransferin thisbranchofmoderntechnologyisofincreasingimportance. Theaimofthe authorsofthisbookistoconcentrateonthephysicalprocesses;thesecanbe developedfromamathematicalpointofview,orfromdirectexperimental- derivedobservation. Thetwoapproachesarecomplementary;eachcanprovide insightsandthesynthesisofthetwocanleadtoaverypowerfulunderstanding oftheprocessesinvolved. Mathematicalmodellingofphysicalprocesseshas hadanimportantroletoplayinthedevelopmentoftechnologyoverthe centuriesandparticularlysointhelastonehundredand?ftyyearsorso. Itcanbearguedthatitismoreimportanttodaythaneverbeforesincethe availabilityofhigh-speedcomputersallowsaccuratenumericalsimulationof industrialprocessesatafractionofthecostofthecorrespondingexperiments. Thisisoneaspectofmathematicalmodelling,highpro?leandmuchvalued, butitisnottheonlyone. Inthepastmathematicalmodellinghadtorelyonqualitativeinves- gation,veryspecialanalyticalsolutions,orinaccurateandtime-consuming calculationsperformedwithlittleinthewayoftabulatedormechanical assistance. Logtablesandsliderulesarestillrememberedbypeopleworking today,thoughtherearesurelyfewwhoregrettheirdisappearance. Thevalueanddistinctivefunctionofmethodsbasedontheanalytical approachisnowbecomingmuchclearer,nowthattheyarenolongerexpected toproducedetailedimitationsofwhathappensinrealexperimentsofind- trialprocesses,afunctionnowful?lledmostlybynumericalmethods,c- sideredbelow. Theemphasistodayisontheirabilitytocon?rmandextend ourunderstandingofthebasicphysicalmechanismsinvolvedintheprocesses of interest. These are essential for any intelligent use of numerical simulation. Theargumentaboutthevalueofteachingpeoplehowtodoarithmetic themselveswithouttheaidofacalculatorseemstobepassingintohistory, vi Preface butitisanimportantoneandprovidesasimpleanalogy. Ifsomeonedoes nothaveafeelingfornumbersandthewayarithmeticworks,theywillalltoo easilyfailtospotanerrorproducedbyamachine. Computersarenotinfallible -andneitherarethosewhobuildorprogramthem. Computersarenow takingonlessmundanemathematicaltasksandthesamecontroversiesare appearinginconnectionwithalgebraicmanipulation. Equally,andwitheven greaterpenaltiesintermsofcostintheeventoferrors,thesameconsiderations applytonumericalsimulationofmajorindustrialprocesses. Awarenessofthe analyticalsolutionscanbeinvaluableindistinguishingtherightfromthe wrong,i. e. forthepractitionertounderstandthebasisofthework,andto haveanideaofthekindsofoutcomesthatareplausible-andtorecognise thosewhicharenot. Thephrase"mathematicalmodelling"is,however,ambiguous,perhaps morenowthanithaseverbeen. Thereisanenormousamountofworkdone todayonsimulationbasedontheuseofverypowerfulcomputerprograms, anditisquitecorrectlyreferredtoasmathematicalmodelling. Theprograms aresometimesconstructedin-housebutareusuallycommercialpackages. This isanentirelyvalidapproachwithspeci?c(generallycommercial)objectives. Ingeneraltherearetwouses. Thedominantobjectiveisnumericalagreement withaparticularexperimentinthe?rstinstance,leadingtopredictivec- mercialuseinthesecondinstance. Thesecondobjectiveistheclari?cation ofphysicalmechanisms,aimedatthegenerationofunderstandingofcomplex interconnectedprocesses,ratherthantheexactreproductionofaparticular experiment. Itissometimesoverlookedthat,withsu?cientcare,anum- icalapproachisequallyvalidintheinvestigationofphysicalfundamentals. Numericalsimulationisnotacentraltopicofthisbook,butbecauseofits crucialimportancetoeachofthetwousestowhichnumericalmodellingcan beput,itisvitalthatthecomputationalbasisoftheworkshouldbec- pletelysound. Inaddition,thelevelofprocessdetailwhichcanbeconsidered bythenumericalapproachusuallyexceedswhatispossiblewiththeanaly- calapproachsigni?cantly,leavinglittlechoicebuttoreverttothenumerical treatmentwheninvestigatingtheinterconnectionsbetweenprocesses. Itis forthesereasonsthatthebookconcludeswithachapteroncomprehensive numericalsimulation. Inmanyways,theapproachadoptedhereiscomplementarytothemore phenomenologicalapproach. Itisalwaysimportantina?eldwhichhasvery directindustrialapplicationstobearinmindhowtechniquessuchasthose describedherewillbeused,butitisessentialnottolosesightofthef- damentals. Thereareserioussafetyimplications;therearecostimplications; therearemoralimplications;thereareconsiderationsoftheappropriateness ofthetechnologytotheapplicationunderconsideration. Aproperrespectfor alltheserequiresanunderstandingofthefundamentals. Wearealltoowellawarethatthisbookdoeslittlemorethanscratch thesurfaceoftheproblemsinvolvedinafundamentalunderstandingofthese phenomena. Ifwehaveprovidedideasandinformationthatcauseothersto Preface vii testthemexperimentallyorintellectually,agreewiththemordisputethem vigorously,anddevelopthemfurther,wewillconsiderthatwehaveachieved ouraim. Colchester April,2008 JohnDowden Contents 1MathematicsinLaserProcessing JohnDowden...1 1. 1 MathematicsanditsApplication...1 1. 2 FormulationinTermsofPartialDi?erentialEquations...3 1. 2. 1 LengthScales...3 1. 2. 2 ConservationEquationsandtheirGeneralisations...4 1. 2. 3 GoverningEquationsofGeneralised ConservationType...7 1. 2. 4 Gauss'sLaw...10 1. 3 BoundaryandInterfaceConditions...11 1. 3. 1 GeneralisedConservationConditions...11 1. 3. 2 TheKinematicConditioninFluidDynamics...13 1. 4 Fick'sLaws...15 1. 5 Electromagnetism...15 1. 5. 1 Maxwell'sEquations...15 1. 5. 2 Ohm'sLaw...18 References...19 2SimulationofLaserCutting WolfgangSchulz,MarkusNiessen,UrsEppelt,KerstinKowalick...21 2. 1 Introduction...22 2. 1. 1 PhysicalPhenomenaandExperimentalObservation...23 2. 2 MathematicalFormulationandAnalysis...26 2. 2. 1 TheOne-PhaseProblem...29 2. 2. 2 TheTwo-PhaseProblem...42 2. 2. 3 Three-PhaseProblem...51 2. 3 Outlook...64 2. 4 Acknowledgements...65 References...65 x Contents 3KeyholeWelding:TheSolidandLiquidPhases AlexanderKaplan...71 3. 1 HeatGenerationandHeatTransfer...71 3. 1. 1 Absorption...

Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.

Availability of advanced computational technology has fundamentally altered the investigative paradigm in the field of biomechanics. Armed with sophisticated computational tools, researchers are seeking answers to fundamental questions by exploring complex biomechanical phenomena at the molecular, cellular, tissue and organ levels. The computational armamentarium includes such diverse tools as the ab initio quantum mechanical and molecular dynamics methods at the atomistic scales and the finite element, boundary element, meshfree as well as immersed boundary and lattice-Boltzmann methods at the continuum scales. Multiscale methods that link various scales are also being developed. While most applications require forward analysis, e.g., finding deformations and stresses as a result of loading, others involve determination of constitutive parameters based on tissue imaging and inverse analysis. This book provides a glimpse of the diverse and important roles that modern computational technology is playing in various areas of biomechanics including biofluids and mass transfer, cardiovascular mechanics, musculoskeletal mechanics, soft tissue mechanics, and biomolecular mechanics.

This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions are tightly interwoven with physical ideas in the treatment of nontrivial boundary value problems for mechanical objects. This second edition includes more extended coverage of the classical and abstract portions of functional analysis. Taken together, the first three chapters now constitute a regular text on applied functional analysis. This potential use of the book is supported by a significantly extended set of exercises with hints and solutions. A new appendix, providing a convenient listing of essential inequalities and imbedding results, has been added. The book should appeal to graduate students and researchers in physics, engineering, and applied mathematics. Reviews of first edition: "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. ... Detailed solutions of the exercises are provided in an appendix." (L'Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises ... test the reader's comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003)

Concrete is still the most widely used construction material since it has the lowest ratio between cost and strength as compared to other available materials. However, it has two undesirable properties, namely: low tensile strength and large brittleness that cause the collapse to occur shortly after the formation of the first crack. To improve these two negative properties and to achieve a partial substitute of conventional reinforcement, an addition of short discontinuous randomly oriented steel fibres can be practiced among others. In spite of positive properties, fibrous concrete did not find such acknowledgment and application as usual concrete. There do not still exist consistent dimensioning rules due to the lack sufficient large-scale static and dynamic experiments taking into account the effect of the fibre orientation. The intention of the book is twofold: first to summarize the most important mechanical and physical properties of steel-fibre-added concrete and reinforced concrete on the basis of numerous experiments described in the scientific literature, and second to describe a quasi-static fracture process at meso-scale both in plain concrete and fibrous concrete using a novel discrete lattice model. In 2D and 3D simulations of fibrous concrete specimens under uniaxial tension, the effect of the fibre volume, fibre distribution, fibre orientation, fibre length, fibrous bond strength and specimen size on both the stress-strain curve and fracture process was carefully analyzed.

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

This book serves both as a textbook and a scientific work. As a textbook, the work gives a clear, thorough and systematic presentation of the fundamental postulates, theorems and principles and their applications of the classical mathematical theories of plasticity and creep. In addition to the mathematical theories, the physical theory of plasticity, the book presents the Budiansky concept of slip and its modification by M. Leonov. Special attention is given to the analysis of the advantages and shortcomings of the classical theories. In its main part, the book presents the synthetic theory of irreversible deformations, which is based on the mathematical Sanders flow plasticity theory and the physical theory, the Budiansky concept of slip. The main peculiarity of the synthetic theory is that the formulae for both plastic and creep deformation, as well their interrelations, can be derived from the single constitutive equation. Furthermore, the synthetic theory, as physical one, can take into account the real processes that take place in solids at irreversible deformation. This widens considerably the potential of the synthetic theory. In the framework of the synthetic theory such problems as creep delay, the Hazen-Kelly effect, the deformation at the break of the load trajectory, the influence of the rate of loading on the stress-strain diagram, creep at the changes of load, creep at unloading and reversed creep, have been analytically described. In the last chapter, the book shows the solution of some contemporary problems of plasticity and creep: Creep deformation at cyclic abrupt changes of temperature, The influence of irradiation on the plastic and creep deformation, Peculiarities of deformation at the phase transformation of some metals.

The idea of this monograph is to present the latest results related to design and analysis of materials and engineering structures. The contributions cover the field of mechanical and civil engineering, ranging from automotive to dam design, transmission towers and up to machine design and exmaples taken from oil industry. Well known experts present their research on damage and fracture of material and structures, materials modelling and evaluation up to image processing and visualization for advanced analyses and evaluation

The fifteen chapters of this book are arranged in a logical progression. The text begins with the more fundamental material on stress and strain transformations with elasticity theory for plane and axially symmetric bodies, followed by a full treatment of the theories of bending and torsion. Coverage of moment distribution, shear flow, struts and energy methods precede a chapter on finite elements. Thereafter, the book presents yield and strength criteria, plasticity, collapse, creep, visco-elasticity, fatigue and fracture mechanics. Appended is material on the properties of areas, matrices and stress concentrations. Each topic is illustrated by worked examples and supported by numerous exercises drawn from the author's teaching experience and professional institution examinations (CEI). This edition includes new material and an extended exercise section for each of the fifteen chapters, as well as three appendices. The broad text ensures its suitability for undergraduate and postgraduate courses in which the mechanics of solids and structures form a part including: mechanical, aeronautical, civil, design and materials engineering.

This book collects peer-reviewed lectures of the IUTAM Symposium on the 100th anniversary of Boundary Layer research. No other reference of this calibre, on this topic, is likely to be published for the next decade. Covers classification, definition and mathematics of boundary layers; instability of boundary layers and transition; boundary layers control; turbulent boundary layers; numerical treatment and boundary layer modelling; special effects in boundary layers.

Lead-free solders are used extensively as interconnection materials in electronic assemblies and play a critical role in the global semiconductor packaging and electronics manufacturing industry. Electronic products such as smart phones, notebooks and high performance computers rely on lead-free solder joints to connect IC chip components to printed circuit boards. Lead Free Solder: Mechanics and Reliability provides in-depth design knowledge on lead-free solder elastic-plastic-creep and strain-rate dependent deformation behavior and its application in failure assessment of solder joint reliability. It includes coverage of advanced mechanics of materials theory and experiments, mechanical properties of solder and solder joint specimens, constitutive models for solder deformation behavior; numerical modeling and simulation of solder joint failure subject to thermal cycling, mechanical bending fatigue, vibration fatigue and board-level drop impact tests.

Programming Finite Elements in Java (TM) teaches the reader how to programme the algorithms of the finite element method (FEM) in Java (TM). The compact, simple code helps the student to read the algorithms, to understand them and thus to be able to refine them. All of the main aspects of finite element techniques are considered: finite element solution; generation of finite element meshes; and visualization of finite element models and results with Java 3D (TM). The step-by-step presentation includes algorithm programming and code explanation at each point. Problems and exercises are provided for each chapter, with Java (TM) source code and problem data sets available from http://extras.springer.com/2010/978-1-84882-971-8.

The Third Conference on Applied Mathematics and Scienti?c Computing took place June 23-27, 2003 on island of Brijuni, Croatia. The main goal of the conference was to interchange ideas among applied mathematicians in the broadest sense both from and outside academia, as well as experts from other areas who apply different mathematical techniques. During the meeting there were invited and contributed talksand software presentations. Invited presentations were given by active researchers from the ?eldsof approximation theory, numerical methods for differential equations and numericallinear algebra. These proceedings contain research and review papers by invited speakers and selected contributed papers from the ?elds of applied and numerical mathematics. A particular aim of the conference was to encourage young scientists to present results of their research. Traditionally, the best presentation given by PhD student was rewarded. This year awardee was Luka Grubisi ? c ' (University of Hagen, Hagen, Germany) and we congratulate him for this achievement. It would be hard to organize the conference without generous support of the Croatian Ministry of Science and Technology and we acknowledge it. We are also indebted to themainorganizer, Department of Mathematics, University of Zagreb.Motivating beautiful nature should bealso mentioned.And,attheend, we are thankful to Drs. JosipTambaca ? and Ivica Nakic ' for giving this book its ?nal shape.

MEMS and Nanotechnology, Volume 6: Proceedings of the 2012 Annual Conference on Experimental and Applied Mechanics represents one of seven volumes of technical papers presented at the Society for Experimental Mechanics SEM 12th International Congress & Exposition on Experimental and Applied Mechanics, held at Costa Mesa, California, June 11-14, 2012. The full set of proceedings also includes volumes on Dynamic Behavior of Materials, Challenges in Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, Imaging Methods for Novel Materials and Challenging Applications, Experimental and Applied Mechanics, Mechanics of Biological Systems and Materials and, Composite Materials and Joining Technologies for Composites.

Thematerialsusedinmanufacturingtheaerospace,aircraft,automobile,andnuclear parts have inherent aws that may grow under uctuating load environments during the operational phase of the structural hardware. The design philosophy, material selection, analysis approach, testing, quality control, inspection, and manufacturing are key elements that can contribute to failure prevention and assure a trouble-free structure. To have a robust structure, it must be designed to withstand the envir- mental load throughout its service life, even when the structure has pre-existing aws or when a part of the structure has already failed. If the design philosophy of the structure is based on the fail-safe requirements, or multiple load path design, partial failure of a structural component due to crack propagation is localized and safely contained or arrested. For that reason, proper inspection technique must be scheduled for reusable parts to detect the amount and rate of crack growth, and the possible need for repairing or replacement of the part. An example of a fail-sa- designed structure with crack-arrest feature, common to all aircraft structural parts, is the skin-stiffened design con guration. However, in other cases, the design p- losophy has safe-life or single load path feature, where analysts must demonstrate that parts have adequate life during their service operation and the possibility of catastrophic failure is remote. For example, all pressurized vessels that have single load path feature are classi ed as high-risk parts. During their service operation, these tanks may develop cracks, which will grow gradually in a stable manner.

Cementitious materials, rocks and fibre-reinforced composites commonly termed as quasibrittle, need a different fracture mechanics approach to model the crack propagation study because of the presence of significant size of fracture process zone ahead of the crack-tip. Recent studies show that concrete structures manifest three important stages in fracture process: crack initiation, stable crack propagation and unstable fracture or failure. Fracture Mechanics concept can better explain the above various stages including the concepts of ductility, size-effect, strain softening and post-cracking behavior of concrete and concrete structures. The book presents a basic introduction on the various nonlinear concrete fracture models considering the respective fracture parameters. To this end, a thorough state-of-the-art review on various aspects of the material behavior and development of different concrete fracture models is presented. The development of cohesive crack model for standard test geometries using commonly used softening functions is shown and extensive studies on the behavior of cohesive crack fracture parameters are also carried out. The subsequent chapter contains the extensive study on the double-K and double-G fracture parameters in which some recent developments on the related fracture parameters are illustrated including introduction of weight function method to Double-K Fracture Model and formulization of size-effect behavior of the double-K fracture parameters. The application of weight function approach for determining of the KR-curve associated with cohesive stress distribution in the fracture process zone is also presented. Available test data are used to validate the new approach. Further, effect of specimen geometry, loading condition, size-effect and softening function on various fracture parameters is investigated. Towards the end, a comparative study between different fracture parameters obtained from various models is presented.

Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author's research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

This concise work provides a general introduction to the design of buildings which must be resistant to the effect of earthquakes. A major part of this design involves the building structure which has a primary role in preventing serious damage or structural collapse. Much of the material presented in this book examines building structures. Due to the recent discovery of vertical components, it examines not only the resistance to lateral forces but also analyses the disastrous influence of vertical components. The work is written for Practicing Civil, Structural, and Mechanical Engineers, Seismologists and Geoscientists. It serves as a knowledge source for graduate students and their instructors.

One of the greatest challenges for mechanists is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, biomedical sciences, and medicine. The proposed workshop will provide an opportunity for computational biomechanics specialists to present and exchange opinions on the opportunities of applying their techniques to computer-integrated medicine. These are peer-reviewed proceedings of the workshop affiliated to a major international research conference (Medical Image Computing and Computer Assisted Intervention MICCAI 2010 in Beijing) dedicated to research in the field of medical image computing and computer assisted medical interventions. The list of subjects covered include: medical image analysis, image-guided surgery, surgical simulation, surgical intervention planning, disease prognosis and diagnostics, injury mechanism analysis, implant and prostheses design, medical robotics.

This book investigates stability loss problems of the viscoelastic composite materials and structural members within the framework of the Three-Dimensional Linearized Theory of Stability (TDLTS). The stability loss problems are considered the development of the initial infinitesimal imperfection in the structure of the material or of the structural members. This development is studied within the framework of the Three-Dimensional Geometrical Non-Linear Theory of the Deformable Solid Body Mechanics. The solution to the corresponding boundary-value problems is presented in the series form in the small parameter which characterizes the degree of the initial imperfection. In this way, the nonlinear problems for the domains bounded by noncanonical surfaces are reduced for the same nonlinear problem for the corresponding domains bounded by canonical surfaces and the series subsequent linearized problems. It is proven that the equations and relations of these linearized problems coincide with the corresponding ones of the well-known TDLTS. Under concrete investigations as stability loss criterion the case is taken for the initial infinitesimal imperfection that starts to increase indefinitely. Moreover, it is proven that the critical parameters can be determined by the use of only the zeroth and first approximations.

This book elucidates how Finite Element methods look like from the perspective of Green's functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green's functions and how approximating of Green's functions. It discusses in detail the discretization error and shows that are coherent with the strategy of "goal oriented refinement". The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

arranged. Among them the following types are met: nanotubes, nanop- ticles, nanopowders, nano?bers, nanowires, nanocomposites, etc. * At the microscale - Microcomposites, such as metal matrix composites (MMCs), ceramic matrix composites (CMCs), alloys or superalloys, s- tered powders, ceramic materials, magnetorheological ?uids (MRFs), etc. * At the macroscale - Macrocomposites, such as functionally graded ma- rials (FGMs), thin layers or ?lms, thermal or oxidation or wear resistant coatings, multilayered structures, long ?ber composites, etc. At each level of analysis a response of the material to any physical excitation may be observed, measured and analyzed. In the sense of innovation of a material, the changes or new ideas can be introduced on the same scale of control (say, atomic or nano) in order to achieve fundamentally new behavior on the other scale of observation (say, micro or macro). For instance, by replacing some similar atoms in the metal crystal str- ture (e. g. Ti-Ti or Al-Al), by unlike atoms in the crystal (e. g. Ti-Al), wi- out the lattice symmetry of the original material changing, new improved properties and characteristics may be observed in intermetallics at the - cro or macroscale (higher speci?c strength, better creep resistance at elevated temperatures, better corrosion resistance, to mention only some properties observed at the macroscale). Similarly, changing material characteristics at the nanoscale, enables creation of completely new material functionality at micro or macroscales (e. g.

The well documented increase in the use of high performance composites as structural materials in aerospace components is continuously raising the demands in terms of dynamic performance, structural integrity, reliable life monitoring systems and adaptive actuating abilities. Current technologies address the above issues separately; material property tailoring and custom design practices aim to the enhancement of dynamic and damage tolerance characteristics, whereas life monitoring and actuation is performed with embedded sensors that may be detrimental to the structural integrity of the component. This publication explores the unique properties of carbon nanotubes (CNT) as an additive in the matrix of Fibre Reinforced Plastics (FRP), for producing structural composites with improved mechanical performance as well as sensing/actuating capabilities. The successful combination of the CNT properties and existing sensing actuating technologies leads to the realization of a multifunctional FRP structure. The current volume presents the state of the art research in this field. The contributions cover all the aspects of the novel composite systems, i.e. modeling from nano to macro scale, enhancement of structural efficiency, dispersion and manufacturing, integral health monitoring abilities, Raman monitoring, as well as the capabilities that ordered carbon nanotube arrays offer in terms of sensing and/or actuating in aerospace composites.

Until now the important concept of quantum chaos has remained somewhat ill defined. This volume tackles the ubiquitous borderline between classical andquantum mechanics, studying in particular the semiclassical limit of chaotic systems. The effects of disorder from dynamics and their relation to stochastic systems, quantum coherence effects in mesoscopic systems, and the relevant theoretical approaches are fruitfully combined in this volume. The major paradigms of what is called quantum chaos, random matrix theory and applications to condensed matter and nuclear physics are presented. Detailed discussions of experimental work with particular emphasis on atomic physics are included. The book is highly recommended for graduate-student seminars.

There have been considerable advances in recent times in understanding many common material processes that are of practical importance, such as nonlinear response, fracture, breakdown, earthquakes, packing, and granular flow, that are of immense practical importance. This has been mainly due to new applications of statistical physics, including percolation theory, fractal concepts and self-organized criticality. This collection of articles brings together research in those closely allied fields. It deals with problems in material science involving random geometries and nonlinearity at a mesoscopic scale, where local disorder and nonlinearity influence the global behaviour of cracks, for example, and problems where randomness in time evolution is as crucial as the geometry itself.