This work gives for the first time an interdisciplinary and deep approach to the mathematical modelling of rubber-like materials considering both the molecular and phenomenological point of views. It contains an introduction to the suitable numerical techniques and an overview of experimental techniques and data with a short survey on some industrial applications. Elastic and inelastic effects are discussed in details. The book is suitable for applied mathematicians, mechanical engineers, civil engineers, material scientists and polymer scientists.
Thermomechanics of Solids and Structures: Physical Mechanisms, Continuum Mechanics, and Applications covers kinematics, balance equations, the strict thermodynamic frameworks of thermoelasticity, thermoplasticity, creep covering constitutive equations, the physical mechanisms of deformation, along with computational aspects. The book concludes with coverage of the thermodynamics of solids and applications of the constitutive three-dimensional model to both one-dimensional homogeneous and composite beam structures. Practical applications of the theories and techniques covered are emphasized throughout the book, with analytical solutions provided for various problems. - Provides foundational knowledge on continuum mechanics, covering kinematics, balance equations, isothermal elasticity and plasticity, variational principles, and more - Presents applications of constitutive 3D models to homogeneous and composite beams, including equations for stress and displacement estimation in thermoelastic beam problems - Reviews experimental results of thermoelastic material behavior, along with case studies to support reviews - Covers the inelastic behavior of materials at elevated temperatures, with experimental results for both monotonic and cyclic tensile tests presented - Looks at the physical mechanisms, experimental results, and constitutive modeling of creep
From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [...] It will be very useful for both mathematicians and physicists." EMS Newsletter
This book provides a concise introduction to soft matter modelling, together with an up-to-date review of the continuum mechanical description of soft and biological materials, from the basics to the latest scientific materials. It also includes multi-physics descriptions, such as chemo-, thermo-, and electro-mechanical coupling. The new edition includes a new chapter on fractures as well as numerous corrections, clarifications and new solutions. Based on a graduate course taught for the past few years at Technion, it presents original explanations for a number of standard materials, and features detailed examples to complement all topics discussed.
The unique properties of elastomeric materials offer numerous advantages in many engineering applications. Elastomeric units are used as couplings or mountings between rigid components, for example in shock absorbers, vibration insulators, flexible joints, seals and suspensions, etc. However, the complicated nature of the behaviour of such material makes it difficult to accurately predict the performance of these units using finite element modelling, for example. It is imperative that constitutive models accurately capture relevant aspects of mechanical behaviour. The latest developments concerning constitutive modelling of rubber is collected in these Proceedings. Topics included in this volume are, Hyperelastic models, Strength, fracture & fatigue, Dynamic properties & the Fletcher-Gent effect, Micro-mechanical & statistical approaches, Stress softening, iscoelasticity, Filler reinforcement, and Tyres, fibre & cord reinforced rubber.
This volume contains the proceedings of the 21st International Congress of Theoretical and Applied Mechanics, ICTAM04, held in Warsaw, in August 2004. Full texts of 27 invited lectures are included. The book captures a snapshot view of the state-of-the-art in the field of contemporary mechanics and will be invaluable to engineers and scientists from a variety of disciplines with interest in the mechanical sciences. The importance of the influence of contemporary mechanics on other branches of sciences becomes evident by browsing through over 60 areas of interest selected as subjects of mini-symposia and pre-nominated sessions. The book gives clear evidence that "...the progress we have achieved together definitely places mechanics on one of the very top locations in the hierarchy of modern research disciplines – with tremendous impact on both our perception of the physical world and the means to implement new technologies so much improving the quality of our life." (M. Kleiber, Opening Speech).
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Chaos in Some Linear Kinetic Models (J Banasiak); Inverse Problems in Photon Transport. Part I: Determination of Physical and Geometrical Features of an Interstellar Cloud (A Belleni-Morante et al.); Inverse Problems in Photon Transport. Part II: Features of a Source Inside an Interstellar Cloud (A Belleni-Morante & R Riganti); The Riemann Problem for a Binary Non-Reacting Mixture of Euler Fluids (F Brini & T Ruggeri); Rate of Convergence toward the Equilibrium in Degenerate Settings (L Desvillettes & C Villani); Asymptotic and Other Properties of Positive Definite Integral Measures for Nonlinear Diffusion (J N Flavin); Thermocapillary Fluid and Adiabatic Waves Near its Critical Point (H Gouin); Constitutive Models for Atactic Elastomers (C O Horgan & G Saccomandi); Considerations about the Gibbs Paradox (I Mller); Transport Coefficients in Stochastic Models of the Revised Enskog and Square-Well Kinetic Theories (J Polewczak & G Stell); Some Recent Mathematical Results in Mixtures Theory of Euler Fluids (T Ruggeri); From Kinetic Systems to Diffusion Equations (F Salvarani & J L Vizquez); Non-Boussinesq Convection in Porous Media (B Straughan); and other papers. Readership: Researchers, academics and graduate students working in the fields of continuum mechanics, wave propagation, stability in fluids, kinetic theory and computational fluid dynamics."
The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.
