The Contact Problem in the Linear Theory of Viscoelasticity when the Time Dependent Contact Area Has Any Number of Maxima and Minima PDF Download
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Author: G. A. C. Graham
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 74
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Book Description
This paper presents a solution to the boundary value problem arising when a rigid punch of arbitrary asymmetric profile is pressed against the surface of a linear viscoelastic half space. The solution, which is valid for a continuously varying contact area with an arbitrary number of montonic increasing maxima and null minima, is expressed in terms of the one parameter family of solutions to the corresponding problem for an elastic half space. The shape of the contact area is always the same as that of some member of the one parameter family of contact areas associated with the corresponding elastic problem. It is shown how the solution may be used to generate specific results for the case of an axisymmetric punch of arbitrary smooth profile. Finally a generalization to viscoelasticity theory of Hertz's theory of the contact of smooth elastic bodies valid for a variable contact area with any number of maxima and minima is given.
Author: G. A. C. Graham
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 74
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Book Description
This paper presents a solution to the boundary value problem arising when a rigid punch of arbitrary asymmetric profile is pressed against the surface of a linear viscoelastic half space. The solution, which is valid for a continuously varying contact area with an arbitrary number of montonic increasing maxima and null minima, is expressed in terms of the one parameter family of solutions to the corresponding problem for an elastic half space. The shape of the contact area is always the same as that of some member of the one parameter family of contact areas associated with the corresponding elastic problem. It is shown how the solution may be used to generate specific results for the case of an axisymmetric punch of arbitrary smooth profile. Finally a generalization to viscoelasticity theory of Hertz's theory of the contact of smooth elastic bodies valid for a variable contact area with any number of maxima and minima is given.
Author: John M. Golden
Publisher: Springer Science & Business Media
ISBN: 3662061562
Category : Science
Languages : en
Pages : 276
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Book Description
The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials. Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology. Early rheological studies isolated the phenomena now labelled as viscoelastic. Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time. On removal of the load, the original length was eventually recovered. He also deduced that the phenomena of stress relaxation and damping of vibrations should occur. Later investigators showed that similar effects may be observed in other materials. The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids". The universal adoption of the term "Viscoelasticity", intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers. The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874).
Author: R. M. Christensen
Publisher: Courier Corporation
ISBN: 0486318966
Category : Technology & Engineering
Languages : en
Pages : 386
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Book Description
Integration of theoretical developments offers complete description of linear theory of viscoelastic behavior of materials, with theoretical formulations derived from continuum mechanics viewpoint and discussions of problem solving. 1982 edition.
Author: Tom Proulx
Publisher: Springer Science & Business Media
ISBN: 1441997946
Category : Technology & Engineering
Languages : en
Pages : 394
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Book Description
This the third volume of six from the Annual Conference of the Society for Experimental Mechanics, 2010, brings together 56 chapters on Time-Dependent Constitutive Fracture and Failure. It presents early findings from experimental and computational investigations on Time Dependent Materials including contributions on Thermal and Mechanical Characterization, Coupled Experimental and Computational Analysis of Fracture Path Selection, Procedures for Mixed Mode Fracture Testing of Bonded Beams, and Experimental Study of Voids in High Strength Aluminum Alloys.
Author: G.A.C. Graham
Publisher: Springer
ISBN: 3709126940
Category : Technology & Engineering
Languages : en
Pages : 317
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Book Description
The main emphasis of these Lecture Notes is on constructing solutions to specific viscoelastic boundary value problems; however properties of the equations of viscoelasticity that provide the theoretical underpinnings for constructing such solutions are also covered. Particular attention is paid to the solution of crack and contact problems. This work is of interest in the context of polymer fracture, modelling of material behaviour, rebound testing of polymers and the phenomenon of hysteretic friction.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 736
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Book Description
Author: Valentin L. Popov
Publisher: Springer
ISBN: 3662587092
Category : Science
Languages : en
Pages : 357
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Book Description
This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.
Author: Y.M. Haddad
Publisher: Springer
ISBN: 9401004366
Category : Science
Languages : en
Pages : 501
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Book Description
This monograph consists of two volumes and provides a unified, comprehensive presentation of the important topics pertaining to the understanding and determination of the mechanical behaviour of engineering materials under different regimes of loading. The large subject area is separated into eighteen chapters and four appendices, all self-contained, which give a complete picture and allow a thorough understanding of the current status and future direction of individual topics. Volume I contains eight chapters and three appendices, and concerns itself with the basic concepts pertaining to the entire monograph, together with the response behaviour of engineering materials under static and quasi-static loading. Thus, Volume I is dedicated to the introduction, the basic concepts and principles of the mechanical response of engineering materials, together with the relevant analysis of elastic, elastic-plastic, and viscoelastic behaviour. Volume II consists of ten chapters and one appendix, and concerns itself with the mechanical behaviour of various classes of materials under dynamic loading, together with the effects of local and microstructural phenomena on the response behaviour of the material. Volume II also contains selected topics concerning intelligent material systems, and pattern recognition and classification methodology for the characterization of material response states. The monograph contains a large number of illustrations, numerical examples and solved problems. The majority of chapters also contain a large number of review problems to challenge the reader. The monograph can be used as a textbook in science and engineering, for third and fourth undergraduate levels, as well as for the graduate levels. It is also a definitive reference work for scientists and engineers involved in the production, processing and applications of engineering materials, as well as for other professionals who are involved in the engineering design process.
Author: George A. C. Graham
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 47
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Book Description
Some well known elastic half space solutions are generalized to encompass arbitrary linear viscoelastic behavior. The viscoelastic material is assumed to be homogeneous and isotropic, and thermal effects are not included. The main part of the survey is devoted to the quasi-static theory whose distinguishing feature is the neglecting of the inertia terms in the equations of motion. Expressions are found for the displacement stress field acting at any point of a viscoelastic half space whose boundary is subjected to an arbitrary time dependent distribution of normal pressure. The solution to the general axisymmetric elastic contact problem given by Sneddon is extended to viscoelasticity theory. Generalizations of the axisymmetric elastic contact problem with friction and Hertz's theory of the contact of smooth elastic bodies are also given. Problems of rolling contact are considered, and some viscoelastic half space problems are solved on the assumption that inertia terms may not be neglected. (Author).
Author: Thomas Richard Rumsey
Publisher:
ISBN:
Category :
Languages : en
Pages : 468
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Book Description
