Non-Linear Elastic Deformations

Non-Linear Elastic Deformations
Author: R. W. Ogden
Publisher: Courier Corporation
Total Pages: 562
Release: 2013-04-26
Genre: Technology & Engineering
ISBN: 0486318710

Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.

Elasticity and Plasticity of Large Deformations

Elasticity and Plasticity of Large Deformations
Author: Albrecht Bertram
Publisher: Springer Nature
Total Pages: 410
Release: 2021-04-07
Genre: Science
ISBN: 3030723283

This book presents an introduction to material theory and, in particular, to elasticity, plasticity and viscoelasticity, to bring the reader close to the frontiers of today’s knowledge in these particular fields. It starts right from the beginning without assuming much knowledge of the subject. Hence, the book is generally comprehensible to all engineers, physicists, mathematicians, and others. At the beginning of each new section, a brief Comment on the Literature contains recommendations for further reading. This book includes an updated reference list and over 100 changes throughout the book. It contains the latest knowledge on the subject. Two new chapters have been added in this new edition. Now finite viscoelasticity is included, and an Essay on gradient materials, which have recently drawn much attention.

Collected Papers of R.S. Rivlin

Collected Papers of R.S. Rivlin
Author: Grigory I. Barenblatt
Publisher: Springer Science & Business Media
Total Pages: 2868
Release: 2013-12-14
Genre: Technology & Engineering
ISBN: 1461224160

R.S. Rivlin is one of the principal architects of nonlinear continuum mechanics: His work on the mechanics of rubber (in the 1940s and 50s) established the basis of finite elasticity theory. These volumes make most of his scientific papers available again and show the full scope and significance of his contributions.

Nonlinear Continuum Mechanics and Large Inelastic Deformations

Nonlinear Continuum Mechanics and Large Inelastic Deformations
Author: Yuriy I. Dimitrienko
Publisher: Springer Science & Business Media
Total Pages: 742
Release: 2010-12-25
Genre: Science
ISBN: 9400700342

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Linear and Non-Linear Deformations of Elastic Solids

Linear and Non-Linear Deformations of Elastic Solids
Author: Arabinda Roy
Publisher: CRC Press
Total Pages: 407
Release: 2019-12-06
Genre: Technology & Engineering
ISBN: 1000758885

Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.

Nonlinear Elasticity

Nonlinear Elasticity
Author: Y. B. Fu
Publisher: Cambridge University Press
Total Pages: 541
Release: 2001-05-07
Genre: Mathematics
ISBN: 0521796954

Comprehensive introduction to nonlinear elasticity for graduates and researchers, covering new developments in the field.

Nonlinear Theory of Elasticity

Nonlinear Theory of Elasticity
Author: Larry Alan Taber
Publisher: World Scientific
Total Pages: 417
Release: 2004
Genre: Science
ISBN: 9812387358

Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.

Contact Problems in Elasticity

Contact Problems in Elasticity
Author: N. Kikuchi
Publisher: SIAM
Total Pages: 508
Release: 1988-01-01
Genre: Science
ISBN: 9781611970845

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.

The Physics of Deformation and Fracture of Polymers

The Physics of Deformation and Fracture of Polymers
Author: A. S. Argon
Publisher: Cambridge University Press
Total Pages: 535
Release: 2013-03-07
Genre: Science
ISBN: 0521821843

A physical, mechanism-based presentation of the plasticity and fracture of polymers, covering industrial scale applications through to nanoscale biofluidic devices.