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| Author | : Morton E. Gurtin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2008-01-20 |
| Genre | : Science |
| ISBN | : 0387226567 |
Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.
| Author | : Gerard A. Maugin |
| Publisher | : CRC Press |
| Total Pages | : 562 |
| Release | : 2016-04-19 |
| Genre | : Mathematics |
| ISBN | : 9781439846131 |
Exploring recent developments in continuum mechanics, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics presents the general framework for configurational forces. It also covers a range of applications in engineering and condensed matter physics. The author presents the fundamentals of accepted standard continuum mechanics, before introducing Eshelby material stress, field theory, variational formulations, Noether’s theorem, and the resulting conservation laws. In the chapter on complex continua, he compares the classical perspective of B.D. Coleman and W. Noll with the viewpoint linked to abstract field theory. He then describes the important notion of local structural rearrangement and its relationship to Eshelby stress. After looking at the relevance of Eshelby stress in the thermodynamic description of singular interfaces, the text focuses on fracture problems, microstructured media, systems with mass exchanges, and electromagnetic deformable media. The concluding chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical-momentum conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics. Written by a long-time researcher in mechanical engineering, this book provides a detailed treatment of the theory of configurational forces—one of the latest and most fruitful advances in macroscopic field theories. Through many applications, it shows the depth and efficiency of this theory.
| Author | : G.A. Maugin |
| Publisher | : CRC Press |
| Total Pages | : 292 |
| Release | : 2020-09-11 |
| Genre | : Mathematics |
| ISBN | : 1000153053 |
Self contained, this book presents a thorough introduction to the complementary notions of physical forces and material (or configurational) forces. All the required elements of continuum mechanics, deformation theory and differential geometry are also covered. This book will be a great help to many, whilst revealing to others a rather new facet of continuum mechanics in general, and elasticity in particular. An organized exposition of continuum mechanics on the material manifold is given which allows for the consideration of material inhomogeneities in their most appropriate framework. In such a frame the nonlinear elasticity of anisotropic inhomogenous materials appears to be a true field theory. Extensions to the cases of electroelasticity and magnetelasticity are then straightforward. In addition, this original approach provides systematic computational means for the evaluation of characteristic parameters which are useful in various branches of applied mechanics and mathematical physics. This is the case for path-independent integrals and energy-release rates in brittle fracture, the influence of electromagnetic fields on fracture criteria (such as in ceramics), the notion of momentum of electromagnetic fields in matter in optics, and the perturbation of solitons propagating in elastic dispersive systems.
| Author | : Sathish Kumar Palaniappan |
| Publisher | : Elsevier |
| Total Pages | : 821 |
| Release | : 2024-08-30 |
| Genre | : Technology & Engineering |
| ISBN | : 0443140863 |
Finite Element Analysis of Polymers and its Composites offers up-to-date and significant findings on the finite element analysis of polymers and its composite materials. It is important to point out, that to date, there are no books that have been published in this concept. Thus, academicians, researchers, scientists, engineers, and students in the similar field will benefit from this highly application-oriented book. This book summarizes the experimental, mathematical and numerical analysis of polymers and its composite materials through finite element method. It provides detailed and comprehensive information on mechanical properties, fatigue and creep behaviour, thermal behaviour, vibrational analysis, testing methods and their modeling techniques. In addition, this book lists the main industrial sectors in which polymers and its composite materials simulation is used, and their gains from it, including aeronautics, medical, aerospace, automotive, naval, energy, civil, sports, manufacturing and even electronics. Expands knowledge about the finite element analysis of polymers and composite materials to broaden application range Presents an extensive survey of recent developments in research Offers advancements of finite element analysis of polymers and composite materials Written by leading experts in the field Provides cutting-edge, up-to-date research on the characterization, analysis, and modeling of polymeric composite materials
| Author | : Donald E. Carlson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 431 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401007284 |
The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.
| Author | : John M. Ball |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 477 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642599389 |
A traditional way to honor distinguished scientists is to combine collections of papers solicited from friendly colleagues into dedicatory volumes. To honor our friend and colleague Mort Gurtin on the occasion of his sixty-fifth birthday, we followed a surer path to produce a work of intrinsic and lasting scientific value: We collected pa pers that we deemed seminal in the field of evolving phase interfaces in solids, a field to which Mort Gurtin himself has made fundamental contributions. Our failure for lack of space to include in this volume every paper of major significance is mitigated by the ma gisterial introduction prepared by Eliot Fried, which assesses the contributions of nu merous works. We hope that this collection will prove useful and stimulating to both researchers and students in this exciting field. August 1998 JohnM. Ball David Kinderlehrer Paulo Podio-Guidugli Marshall Slemrod Contents Introduction: Fifty Years of Research on Evolving Phase Interfaces By Eliot Fried. 0 •••••••••••••••••••••••••••••••••••••••••••••••• 0 ••••• 1 I. Papers on Materials Science Surface Tension as a Motivation for Sintering By C. Herring 33 Two-Dimensional Motion of Idealized Grain Boundaries By W. W. Mullins 0 ••••••••••• 0 ••••••••••••••••••• 70 Morphological. Stability of a Particle Growing by Diffusion or Heat Flow By w. w. Mullins and R. F. Sekerka 75 Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics By J. D. Eshelby 82 The Interactions of Composition and Stress in Crystalline Solids By F. e. Larche and 1. W. Cahn 120 II.
| Author | : Stefan Diebels |
| Publisher | : Springer |
| Total Pages | : 183 |
| Release | : 2019-02-01 |
| Genre | : Science |
| ISBN | : 366257957X |
Due to their high stiffness and strength and their good processing properties short fibre reinforced thermoplastics are well-established construction materials. Up to now, simulation of engineering parts consisting of short fibre reinforced thermoplastics has often been based on macroscopic phenomenological models, but deformations, damage and failure of composite materials strongly depend on their microstructure. The typical modes of failure of short fibre thermoplastics enriched with glass fibres are matrix failure, rupture of fibres and delamination, and pure macroscopic consideration is not sufficient to predict those effects. The typical predictive phenomenological models are complex and only available for very special failures. A quantitative prediction on how failure will change depending on the content and orientation of the fibres is generally not possible, and the direct involvement of the above effects in a numerical simulation requires multi-scale modelling. One the one hand, this makes it possible to take into account the properties of the matrix material and the fibre material, the microstructure of the composite in terms of fibre content, fibre orientation and shape as well as the properties of the interface between fibres and matrix. On the other hand, the multi-scale approach links these local properties to the global behaviour and forms the basis for the dimensioning and design of engineering components. Furthermore, multi-scale numerical simulations are required to allow efficient solution of the models when investigating three-dimensional problems of dimensioning engineering parts. Bringing together mathematical modelling, materials mechanics, numerical methods and experimental engineering, this book provides a unique overview of multi-scale modelling approaches, multi-scale simulations and experimental investigations of short fibre reinforced thermoplastics. The first chapters focus on two principal subjects: the mathematical and mechanical models governing composite properties and damage description. The subsequent chapters present numerical algorithms based on the Finite Element Method and the Boundary Element Method, both of which make explicit use of the composite’s microstructure. Further, the results of the numerical simulations are shown and compared to experimental results. Lastly, the book investigates deformation and failure of composite materials experimentally, explaining the applied methods and presenting the results for different volume fractions of fibres. This book is a valuable resource for applied mathematics, theoretical and experimental mechanical engineers as well as engineers in industry dealing with modelling and simulation of short fibre reinforced composites.
| Author | : U. Klein |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 290 |
| Release | : 2013-04-17 |
| Genre | : Philosophy |
| ISBN | : 9401597375 |
constitutive of reference in laboratory sciences as cultural sign systems and their manipulation and superposition, collectively shared classifications and associated conceptual frameworks,· and various fonns of collective action and social institutions. This raises the question of how much modes of representation, and specific types of sign systems mobilized to construct them, contribute to reference. Semioticians have argued that sign systems are not merely passive media for expressing preconceived ideas but actively contribute to meaning. Sign systems are culturally loaded with meaning stemming from previous practical applications and social traditions of applications. In new local contexts of application they not only transfer stabilized meaning but also can be used as active resources to add new significance and modify previous meaning. This view is supported by several analyses presented in this volume. Sign systems can be implemented like tools that are manipulated and superposed with other types of signs to forge new representations. The mode of representation, made possible by applying and manipulating specific types of representational tools, such as diagrammatic rather than mathematical representations, or Berzelian fonnulas rather than verbal language, contributes to meaning and forges fine-grained differentiations between scientists' concepts. Taken together, the essays contained in this volume give us a multifaceted picture of the broad variety of modes of representation in nineteenth-century and twentieth-century laboratory sciences, of the way scientists juxtaposed and integrated various representations, and of their pragmatic use as tools in scientific and industrial practice.
| Author | : Ansgar Beckermann |
| Publisher | : Walter de Gruyter |
| Total Pages | : 325 |
| Release | : 2011-07-20 |
| Genre | : Philosophy |
| ISBN | : 3110870088 |
| Author | : José Merodio |
| Publisher | : EOLSS Publications |
| Total Pages | : 388 |
| Release | : 2011-11-30 |
| Genre | : |
| ISBN | : 1848263740 |
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.
