[PDF] Boundary Layers In Strain Gradient Theory Of Linear Elasticity eBook

Author : Michael A. Sadowsky
Publisher :
Page : 73 pages
File Size : 20,36 MB
Release : 1967
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In a previous technical report based on couple stress theory the presence of an elastic boundary layer of minute thickness was established in which the states of stress and displacement differ essentially and significantly from classical elasticity solutions. The boundary layer effect becomes dominant for microbodies in composites. Based on strain-gradient theory a reinvestigation of the phenomena in elastic boundary layers is presented. Due to the fact that no reliable information on micromoduli is available, a mathematical parameter m is introduced which makes it convenient to compare the strain-gradient results (0m

Author : Frederick D. Day
Publisher :
Page : 84 pages
File Size : 10,27 MB
Release : 1966
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An analytic solution is obtained for two composite-body problems employing the strain-gradient theory of elasticity as developed by Mindlin. The investigation is concerned with the effects produced by strain-gradients, especially bonding stresses in the vicinity of an interface separating two dissimilar materials when higher order contact conditions prevail at the common boundary. The composite body under consideration consists of an infinite elastic strip ('microlayer') embedded in two semi-infinite elastic regions. The first problem concerns the case of uniform tension at infinity applied in a direction perpendicular to the microlayer. The second considers simple shear applied at infinity parallel to the microlayer. It is shown that the stresses that develop in the vicinity of an interface may be at large variance with the classical results. The magnitude of these stresses may be many times greater than the classical values, thus emphasizing the uncertainty of the classical approach in this instance. This variance is very significant when one material is much more rigid than the other, as encountered in the practical case of composite materials.

Author : Michele Ciarletta
Publisher : CRC Press
Page : 363 pages
File Size : 24,4 MB
Release : 2020-11-26
Category : Mathematics
ISBN : 1000158063

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Problems concerning non-classical elastic solids continue to attract the attention of mathematicians, scientists and engineers. Research in this area addresses problems concerning many substances, such as crystals, polymers, composites, ceramics and blood. This comprehensive, accessible work brings together recent research in this field, and will be of great interest to mathematicians, physicists and other specialists working in this area.

Author : D. Iesan
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 32,53 MB
Release : 2013-03-19
Category : Science
ISBN : 1402023103

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This volume is concerned with the basic problems of the theory of thermoelasticity for three models of continuous bodies: materials with voids, micropolar solids and nonsimple bodies. Beginning with the basic laws of thermodynamics, the theory of thermoelastic materials with voids is treated. Two subsequent chapters cover the analysis of the linear theory of micropolar thermoelastic bodies. The book concludes with a study of nonsimple thermoelastic materials, which are characterised by the inclusion of higher gradients of displacement in the basic postulates. Relevant examples and exercises which illustrate the theory are given throughout the text. The book should be of interest to mathematicians and specialists working in the fields of elasticity, thermoelasticity, civil engineering and geophysics.

Author : Morton E. Gurtin
Publisher : Cambridge University Press
Page : 721 pages
File Size : 48,23 MB
Release : 2010-04-19
Category : Science
ISBN : 1139482157

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The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Author : K. H. Chang
Publisher :
Page : 31 pages
File Size : 47,17 MB
Release : 1971
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In the Report, boundary layer techniques - familiar in the context of fluid mechanics - are applied to two-dimensional couple-stress theory of linear elasticity. The existence of a 'boundary layer' is established, and it is shown that in the interior the solutions approach rapidly the corresponding solutions of the classical elasticity theory. The practical application of the method is illustrated for simple shear and Lame-type problems. (Author).

Author : Albrecht Bertram
Publisher : Springer Nature
Page : 177 pages
File Size : 26,88 MB
Release : 2020-06-30
Category : Science
ISBN : 3030438309

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Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories involving the higher order gradient of the strain tensor, or of plastic strain. It begins by reviewing experimental findings on the existence (or non-existence) of size effects on the mechanics of materials. In turn, the book devises first, second and higher order strain gradient theories from general principles, and presents constitutive frameworks that satisfy thermodynamic requirements. The special case of strain gradient plasticity is then developed and illustrated via computational analyses of size effects on the plasticity of metals at small scales. In closing, the book explains the origin of gradient effects in the case of lattice structures by drawing on homogenization theory.

Author :
Publisher :
Page : 1460 pages
File Size : 47,78 MB
Release : 1991
Category : Aeronautics
ISBN :

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Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.