Experimental Mechanics of Composite, Hybrid, and Multifunctional Materials: Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, the sixth volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on a wide range of areas, including: Characterization of Energy Storage Materials Microvascular & Natural Composites Nanocomposites for Multifunctional Performance Composite/Hybrid Characterization Using Digital Image Correlation Failure Behavior of Polymer Matrix Composites Non-Destructive Testing of Composites Composite Test Methods Joints/Bonded Composites

Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8: Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, the eighth volume of eight from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on a wide range of areas, including: Advances in Residual Stress Measurement Methods Residual Stress Effects on Material Performance Optical, Ultrasonic, and Diffraction Methods for Residual Stress Measurement Thermomechanics & Infrared Imaging Inverse Methods Inverse Methods in Plasticity Applications in Experimental Mechanics

Introduction to Solid Mechanics: An Integrated Approach presents for the first time in one text the concepts and processes covered in statics and mechanics of materials curricula following a granular, topically integrated approach. Since the turn of the millennium, it has become common in engineering schools to combine the traditional undergraduate offerings in rigid-body statics (usually called "statics") and deformable body mechanics (known traditionally as "strength of materials" or, more recently, "mechanics of materials") into a single, introductory course in solid mechanics. Many textbooks for the new course sequentially meld pieces of existing, discrete books--sometimes, but not always, acknowledging the origin--into two halves covering Statics and Mechanics of Materials. In this volume, Professors Lubliner and Papadopoulos methodically combine the essentials of statics and mechanics of materials, illustrating the relationship of concepts throughout, into one "integrated" text. Introduction to Solid Mechanics: An Integrated Perspective offers a holistic treatment of the depth and breadth of solid mechanics, proceeding from first principles to applications.

The book presents state-of-the-art works in computational engineering. Focus is on mathematical modeling, numerical simulation, experimental validation and visualization in engineering sciences. In particular, the following topics are presented: constitutive models and their implementation into finite element codes, numerical models in nonlinear elasto-dynamics including seismic excitations, multiphase models in structural engineering and multiscale models of materials systems, sensitivity and reliability analysis of engineering structures, the application of scientific computing in urban water management and hydraulic engineering, and the application of genetic algorithms for the registration of laser scanner point clouds.

Presenting a state-of-the-art overview of theoretical and computational models that link characteristic biomechanical phenomena, this book provides guidelines and examples for creating multiscale models in representative systems and organisms. It develops the reader's understanding of and intuition for multiscale phenomena in biomechanics and mechanobiology, and introduces a mathematical framework and computational techniques paramount to creating predictive multiscale models. Biomechanics involves the study of the interactions of physical forces with biological systems at all scales - including molecular, cellular, tissue and organ scales. The emerging field of mechanobiology focuses on the way that cells produce and respond to mechanical forces - bridging the science of mechanics with the disciplines of genetics and molecular biology. Linking disparate spatial and temporal scales using computational techniques is emerging as a key concept in investigating some of the complex problems underlying these disciplines. Providing an invaluable field manual for graduate students and researchers of theoretical and computational modelling in biology, this book is also intended for readers interested in biomedical engineering, applied mechanics and mathematical biology.

This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design. After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks. In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids. In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures. This book is part of a series on "Mathematics for Industry" and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications.

This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.

Andreas Hazir is investigating the door seal contribution to the interior noise level of production vehicles. These investigations contain experimental contribution analyses of real production vehicles and of academic test cases as well as the development of a simulation methodology for noise transmission through sealing systems and side windows. The simulations are realized by coupling transient computational aeroacoustics of the exterior flow to nonlinear finite element simulations of the structural transmission. By introducing a linear transmission model, the setup and computational costs of the seal noise transmission are significantly reduced, resulting in the feasibility of numerical contribution analyses of real production vehicles.

In this second edition a new chapter has been added covering the buffeting theory in a finite element format. The motivation for this has been that a finite element format is becoming more and more dominant in all areas of structural mechanics. It is streamlined for computer programming, and it facilitates the use of general purpose routines that are applicable in several types of structural engineering problems. In this book the finite element formulation of the problem of dynamic response calculations follows the general principle of virtual work, a general principle which may be found in many other text books. While the buffeting wind load itself has with no trouble been included in a finite element format, the main challenge has been to obtain a consistent formulation that includes all the relevant motion induced forces. This has been important, because, while many structures (e.g. long-span suspension bridges) may suffer greatly and become unstable at high wind velocities, the same structures may also benefit from these effects at the design wind velocity. It is well known that motion induced forces will change the stiffness and damping properties of the combined structure and flow system. If calculations are performed for a suitably close set of increasing mean wind velocities and the changing mechanical properties (stiffness and damping) are updated from one velocity to the next, then the response of the system may be followed up to wind velocities close to the stability limit, i.e. up to response values that are perceived as unduly large. Finite element calculations may be performed in time domain, in frequency domain or converted into a modal format. All these options have been included. Pursuing a time domain solution strategy requires the use of the so-called indicial functions. The theory behind such a formulation is also covered, and the determination of these functions from aerodynamic derivatives has been included in a separate appendix.

A molecular view on the fundamental issues in polymer physics is provided with an aim at students in chemistry, chemical engineering, condensed matter physics and material science courses. An updated translation by the author, a renowned Chinese chemist, it has been proven to be an effective source of learning for many years. Up-to-date developments are reflected throughout the work in this concise presentation of the topic. The author aims at presenting the subject in an efficient manner, which makes this particularly suitable for teaching polymer physics in settings where time is limited, without having to sacrifice the extensive scope that this topic demands.

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: "The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory." (ZAMM, 2002) "In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field." (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Die Casting: An Analytical Approach will refresh knowledge of the governing laws of the fluid dynamics that have an effect on die cast die and die cast process design. It will be bought by product designers that design die cast parts and die cast die and process engineers and designers.

In the last few years, a significant increase in applications of MMCs has taken place, particularly in the areas of automotive, aerospace, electronics, and recreation. These include continuous fiber reinforced MMCs for cables in power transmission, high temperature superconducting wires, particulate MMCs in civilian aircraft and automotive applications, and high volume fraction, high thermal conductivity substrates for electronic packaging. Nevertheless, as with any novel material systems, there is a lack of fundamental understanding on the part of practicing engineers and designers. This book would seek to address these issues, in a thorough and cohesive manner, as well as to provide students and scientists with a basic understanding of MMCs. This book will emphasize the synergistic relationships among processing, structure, and properties of metal matrix composites.

This is a book for people who love mechanics of composite materials and ? MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing the numerical calculations needed in mechanics of c- posite materials. In particular, the steps of the mechanical calculations will be emphasized in this book. The reader will not ?nd ready-made MATLAB programs for use as black boxes. Instead step-by-step solutions of composite material mechanics problems are examined in detail using MATLAB. All the problems in the book assume linear elastic behavior in structural mechanics. The emphasis is not on mass computations or programming, but rather on learning the composite material mechanics computations and understanding of the underlying concepts. The basic aspects of the mechanics of ?ber-reinforced composite materials are covered in this book. This includes lamina analysis in both the local and global coordinate systems, laminate analysis, and failure theories of a lamina.

st The21 InternationalCongressofTheoreticalandAppliedMechanics (ICTAM04) took place August 15 - 21, 2004, in Warsaw, Poland. It was organized by Polish National Committee of IUTAM, Institute of Fundamental Technological Research of the Polish Academy of Sciences (IPPTPAN)andWarsawUniversityofTechnology. TheCongressvenue was the main building of Warsaw University of Technology. The idea of congresses devoted to mechanics, can be traced back to a conference on problems of?uid mechanics in Innsbruck, 1922. It was organized by four individuals, whose names, are and will, remain very wellknowntonextgenerationsofscientists,C.W.Oseen,T.Levi-Civite, T.vonKarm ' ' ' an,andL.Prandtl. Thisconferencewassofruitful,thatthe organizers decided to arrange similar meetings in the future, every four years, and to extend the scope of the future meetings to include solid mechanics. Hence a series of meetings started eighty years agowiththe st 1 ICTAM held in Delft, Netherlands. From the meetingsoftheCongress Committee sprang the idea of a more permanent organization to look out for the world interests in the mechanical sciences. Thus, IUTAM, theInternational Unionof Theor- ical and Applied Mechanics, was formed on September 26, 1946. In 1947 IUTAM became a member of ICSU, the International Council of Sci- ti?c Unions, itself founded in 1931. The highest authority of IUTAMis the General Assembly, with delegates from the Adhering Organizations, each of which is a?liated with a national learned society in a given country. Scienti?cProgram Contemporary mechanics poses both, the fundamental problems from the area of pure science, and its strong links with modern technology.

One of the key aspects of this volume is to cut across the traditional taxonomy of disciplines in the study of alloys. Hence there has been a deliberate attempt to integrate the different approaches taken towards alloys as a class of materials in different fields, ranging from geology to metallurgical engineering. The emphasis of this book is to highlight commonalities between different fields with respect to how alloys are studied. The topics in this book fall into several themes, which suggest a number of different classification schemes. We have chosen a scheme that classifies the papers in the volume into the categories Microstructural Considerations, Ordering, Kinetics and Diffusion, Magnetic Considerations and Elastic Considerations. The book has juxtaposed apparently disparate approaches to similar physical processes, in the hope of revealing a more dynamic character of the processes under consideration. This monograph will invigorate new kinds of discussion and reveal challenges and new avenues to the description and prediction of properties of materials in the solid state and the conditions that produce them.

This volume contains the articles presented at the 18th International Meshing Roundtable (IMR) organized, in part, by Sandia National Laboratories and held October 25-28, 2009 in Salt Lake City, Utah, USA. The volume presents recent results of mesh generation and adaptation which has applications to finite element simulation. It introduces theoretical and novel ideas with practical potential.

Cracks can develop in rotating shafts and can propagate to relevant depths without affecting consistently the normal operating conditions of the shaft. In order to avoid catastrophic failures, accurate vibration analyses have to be performed for crack detection. The identification of the crack location and depth is possible by means of a model based diagnostic approach, provided that the model of the crack and the model of the cracked shaft dynamical behavior are accurate and reliable. This monograph shows the typical dynamical behavior of cracked shafts and presents tests for detecting cracks. The book describes how to model cracks, how to simulate the dynamical behavior of cracked shaft, and compares the corresponding numerical with experimental results. All effects of cracks on the vibrations of rotating shafts are analyzed, and some results of a numerical sensitivity analysis of the vibrations to the presence and severity of the crack are shown. Finally the book describes some crack identification procedures and shows some results in model based crack identification in position and depth. The book is useful for higher university courses in mechanical and energetic engineering, but also for skilled technical people employed in power generation industries.

This book deals with the management of calculations in linear and nonlinear mechanics. Particular attention is given to error estimators and indicators for structural analysis. The accent is on the concept of error in constitutive relation. An important part of the work is also devoted to the utilization of the error estimators involved in a calculation, beginning with the parameters related to the mesh. Many of the topics are taken from the most recent research by the authors: local error estimators, extention of the concept of error in constitutive relation to nonlinear evolution problems and dynamic problems, adaptive improvement of calculations in nonlinear mechanics. This work is intended for all those interested in mechanics: students, researchers and engineers concerned with the construction of models as well as their simulation for industrial purposes.

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.