Author : Victor A. Eremeyev
Publisher : Springer Science & Business Media
Page : 145 pages
File Size : 46,87 MB
Release : 2012-07-25
Category : Science
ISBN : 3642283535
The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the constitutive modeling, i.e. constitutive inequalities, symmetry groups, acceleration waves, etc.
Author : A. Cemal Eringen
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 17,57 MB
Release : 2012-12-06
Category : Science
ISBN : 1461205557
Microcontinuum field theories extend classical field theories to microscopic spaces and short time scales. This volume is concerned with the kinematics of microcontinua. It begins with a discussion of strain, stress tensors, balance laws, and constitutive equations, and then discusses applications of the fundamental ideas to the theory of elasticity. The ideas developed here are important in modeling the fluid or elastic properties of porous media, polymers, liquid crystals, slurries, and composite materials.
Author : Ioannis Vardoulakis (Deceased)
Publisher : Springer
Page : 183 pages
File Size : 10,84 MB
Release : 2018-08-01
Category : Science
ISBN : 3319951564
This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.
Author : Holm Altenbach
Publisher : Springer
Page : 799 pages
File Size : 30,37 MB
Release : 2018-03-24
Category : Science
ISBN : 3319724401
This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.
Author : Antonio Romano
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 40,9 MB
Release : 2010-07-23
Category : Science
ISBN : 0817648704
This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.
Author : Martin Ostoja-Starzewski
Publisher : CRC Press
Page : 500 pages
File Size : 38,89 MB
Release : 2007-08-13
Category : Mathematics
ISBN : 1420010271
An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomness. Using this approach, Microstructural Randomness and Scaling in Mechanics of Materials explores numerous stochastic models and methods used in the m
Author : Grzegorz Lukaszewicz
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 45,58 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 1461206413
Micropolar fluids are fluids with microstructure. They belong to a class of fluids with nonsymmetric stress tensor that we shall call polar fluids, and include, as a special case, the well-established Navier-Stokes model of classical fluids that we shall call ordinary fluids. Physically, micropolar fluids may represent fluids consisting of rigid, randomly oriented (or spherical) particles suspended in a viscous medium, where the deformation of fluid particles is ignored. The model of micropolar fluids introduced in [65] by C. A. Eringen is worth studying as a very well balanced one. First, it is a well-founded and significant generalization of the classical Navier-Stokes model, covering, both in theory and applications, many more phenomena than the classical one. Moreover, it is elegant and not too complicated, in other words, man ageable to both mathematicians who study its theory and physicists and engineers who apply it. The main aim of this book is to present the theory of micropolar fluids, in particular its mathematical theory, to a wide range of readers. The book also presents two applications of micropolar fluids, one in the theory of lubrication and the other in the theory of porous media, as well as several exact solutions of particular problems and a numerical method. We took pains to make the presentation both clear and uniform.
Author : Holm Altenbach
Publisher : Springer
Page : 463 pages
File Size : 50,68 MB
Release : 2018-01-04
Category : Science
ISBN : 3319705636
This book presents a collection of contributions on the advanced mechanics of materials and mechanics of structures approaches, written in honor of Professor Kienzler. It covers various topics related to constitutive models for advanced materials, recent developments in mechanics of configuration forces, as well as new approaches to the efficient modeling and analysis of engineering structures.
Author : Holm Altenbach
Publisher : Springer Nature
Page : 424 pages
File Size : 29,24 MB
Release :
Category :
ISBN : 3031490436
Author : Janusz Dyszlewicz
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 34,82 MB
Release : 2004-02-11
Category : Technology & Engineering
ISBN : 9783540418351
The monograph "Micropolar Theory of Elasticity" is devoted to the asymmetric theory of elasticity and thermoelasticity, aiming at researchers and postgraduate students in solid mechanics and applied mathematics, as well as mechanical engineers. It offers various new results including the basic field equations, general methods of integration of basic equations, formulations of problems, as well as solutions to particular problems. The presented general solutions cover those of Galerkin, Green-Lamé and Papkovitch-Neuber type, whereas the formulations include the displacement-rotation problems as well as pure stress problems of asymmetric elastodynamics. Solutions to stationary 3D and 2D problems for a half-space, and singular solutions to 3D and 2D asymmetric elastodynamics and the thermoelasto-dynamics problems for an infinite space are given.
