We assume adhesion between the elastic solid and the punch and we study the deformation as the punch is retracted. In engineering, deformation refers to the change in size or shape of an object. What is deformation, the deformation gradient, homogenous deformations, constructing the deformation gradient using dyads, polar decomposition, strain, example. Continuum mechanics of large deformation contact springerlink. Modern numerical methods are able to simulate large mass movements and there is an opportunity to utilise such methods to evaluate the risks of catastrophic damage if a landslide occurs.
Large deformation kinematics pdf 66p this book covers the following topics. Mortar finite element methods for large deformation. A model membrane contact system consisting of an acrylic copolymer membrane and a pdms substrate was utilized to evaluate a recently developed nonlinear largedeformation adhesive contact analysis. Large deformation and strain gradient fracture analysis of. A surfacetosurface finite element algorithm for large. Journal of the mechanics and physics of solids, vol. Mortar finite element methods provide a very convenient and powerful discretization framework for geometrically nonlinear applications in computational contact mechanics, because they allow for a variationally consistent treatment of contact conditions mesh tying, nonpenetration, frictionless or frictional sliding despite the fact that the underlying contact surface meshes are nonmatching. An introduction to continuum mechanics, academic press, 1981.
The undeformed membrane is flat and has uniform initial thickness h 0. Trends in largedeformation analysis of landslide mass. Download mechanics of solids and materials pdf genial ebooks. This important work covers the fundamentals of finite deformation in solids and constitutive relations for different types of stresses in large deformation of solids. Large deformation classical and computational solid. In stick no relative motion occurs between contacting points, thus, the intersection point x 2 on.
Mechanical analysis of deformation analysis of deformation in solid mechanics. Pdf contact mechanics is a fundamental field of tribology and. The op spoke of large material deformation iirc, and i do not see that as necessarily implying nonlinear. The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. A finite strain theory, also called large strain theory, large deformation theory, deals with deformations in which both rotations and strains are arbitrarily large. In addition, a linear buckling analysis is performed and the critical load obtained from this study is compared with eulers critical load. The initial configuration of the membrane is flat and circular and is clamped at the edge. Khoei ar, mousavi smt 2010 modeling of large deformationlarge sliding contact via the penalty xfem technique. The contact constraints are treated with a mortarbased approach combined with a simplified integration method avoiding segmentation of the contact surfaces, and the discretization of the continuum is performed with arbitrary order nurbs and lagrange polynomial elements. The continuum shell element is utilized in the numerical simulations of isotropic, laminated composite and functionally graded materials, using a highorder spectralhp approximations.
In this sense, mackerle presented a summary on the use of fem for indentation problems, a specificity of contact mechanics. Hence contact mechanics has, from an engineering point of view, a long history, beginning in ancient egypt with the movement of large stone. The crld cable, patented by professor he manchao and his teams, is actually a compound device consisting of following elements. In the preceding chapter, a nonlinear finite element formulation for the large deformation analysis was presented. The governing equations with relevant boundary conditions for a piezoelectric cantilever beam with simultaneous consideration of surface piezoelectricity, surface elasticity, surface. This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or. This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. No one can walk without frictional contact, and no car would move for the same r son.
A configuration is a set containing the positions of all particles of the body. Static pull testing of a new type of large deformation. Numerical modeling of accretionary wedge mechanics. The advancing in contact mechanics for modeling different deformation regimes depended on the development of computational simulation tools, especially the finite element method fem. Displacements are the absolute change in position of a point on the object. Dec 08, 20 large deformation and adhesive contact studies of axisymmetric membranes. Strain is the relative internal change in shape of an infinitesimally small cube of material and can be expressed as a nondimensional change in length or angle of. A contact domain method for large deformation frictional. In this paper, various largedeformation analysis methods are introduced and their applicability for solving landslide problems is discussed. On lagrangian mechanics and the implicit material point. Large deformation kinematics pdf 66p download book. A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies surfaces known as the normal direction and frictional stresses acting tangentially between the surfaces. In addition, modelling and simulation is covered to create an indepth and epistemological understanding of the process.
In addition to stationary contact, an appreciable section of the book is concerned with. The updated lagrangian formulation is used to model the large deformation. The analysis of deformation is fundamental to the study of all solid mechanics problems. Plastic strain ratio of yield strength to effective elastic modulus. A mortar formulation for 3d large deformation contact. Mathematical, physical and engineering sciences 20, 469 2160, 20424. A deformation may be caused by external loads, body forces such as gravity or electromagnetic forces, or changes in temperature, moisture content, or chemical reactions, etc. A hybrid finite element formulation for largedeformation contact. Deflection is the relative change in external displacements on an object. Large deformation in solid mechanics page 2 physics forums. Penalty approach is employed to impose the contact constraints and nonpenetration condition at the material interfaces.
Thus, employing them for solving contact mechanics problems involving thin structures and almost. It covers material processing and describes several related industrial applications. Consider the planestrain deformation of an infinitely long elastic membrane of initial width 2a subjected to uniform excess pressure i. Soft thermoplastics have a rather large plastic deformation range as do ductile metals such as copper, silver, and gold. Large deformation adhesive contact mechanics of circular. Analysis of deformation in solid mechanics the analysis of deformation is fundamental to the study of all solid mechanics problems.
Khoei ar, mousavi smt 2010 modeling of large deformation large sliding contact via the penalty xfem technique. The results are compared with each other and with a benchmark solution from nafems. The technique employs an integral projection of contact variables on the contact surface to provide a consistent representation of all contact variables over a single discretization. This book blends both innovative large strain, strain rate, temperature, time dependent deformation and localized plastic deformation in crystalline solids, deformation of biological networks and traditional elastic theory of torsion, elastic beam and plate theories, contact mechanics topics in a coherent theoretical framework. An object in the plastic deformation range, however, will first have undergone elastic deformation, which is undone simply be removing the applied force, so the object will return part way to its original shape. This page focuses mainly on the normal direction, i. The international symposium on deformation and progressive failure in geomechanics provided an opportunity for discussing recent advances in this area. The beam is modeled using both the solid mechanics interface and the beam interface.
Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. In addition, modelling and simulation is covered to create an indepth and. This formulation, which is consistent with the motion description used in the theory of continuum mechanics and can be used to correctly describe an arbitrary rigidbody motion, leads to a constant mass matrix and nonlinear vector of elastic forces. A mortar formulation for 3d large deformation contact using. In the preceding chapter, a nonlinear finite element formulation for the largedeformation analysis was presented. On the other hand,the op was asking about nonlinear elastic material behavior.
Progressive failure has been a classical problem in the field of geotechnical engineering and has attracted considerable attention in connection with slope stability and foundation problems. Large deformation contact mechanics of a pressurized long. Jan 16, 2018 computational continuum mechanics, third edition is designed to function equally well as a text for advanced undergraduates and firstyear graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, bio mechanics, computational biology, multibody system dynamics, and. Each chapter of both books contains a summary of essential formulae which are developed within the chapter and a large number of worked examples. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. A new 12parameter shell finite element for large deformation analysis of shell structures is developed using thirdorder thickness stretch kinematics. Large deformation of soft elastic materials in adhesive. Nonconforming elastic bodies in contact whose deformation is sufficiently small for the linear small strain theory of elasticity to be applicable inevitably make contact over an area whose dimensions are small compared with the radii of curvature of the undeformed surfaces. In this work, a mortar finite element formulation is developed for solving large deformation frictional contact problems in a robust and accurate manner.
Mortar finite element methods for large deformation contact mechanics by bin yang author isbn. Download mechanics of solids and materials pdf genial. Mechanics of engineering materials pdf free download. Although eachchapter is selfcontained,in the first half of the book, each chapter builds on the previous oneas the principlesare established, while the second half of the book appliestheseprinciplesin specificareas. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics. The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact. Behavior, performance, modeling and control focuses on deformation based process behaviors and process performance in terms of the quality of the needed shape, geometries, and the requested properties of the deformed products. The vonmises yield criterion is used to model the elastoplastic behavior assuming isotropic hardening. Large displacement or large rotation theory, which assumes small strains but large rotations and displacements.
In this paper, various large deformation analysis methods are introduced and their applicability for solving landslide problems is discussed. Contact mechanics has its application in many engineering problems. If the address matches an existing account you will receive an email with instructions to reset your password. A large strain finite element analysis is used to study the deformation of an incompressible neohookean half space in contact with a flat rigid cylindrical punch. The engineering strain is the most common definition applied to materials used in mechanical and structural engineering, which are subjected to very small deformations. Equations and describe searching for evolving contact and are only valid during slip. Deformation analysis of plates on unilateral elastic. Line loading of an elastic halfspace chapter 2 contact.
Computational continuum mechanics, third edition is designed to function equally well as a text for advanced undergraduates and firstyear graduate students and as a working reference for researchers, practicing engineers, and scientists working in computational mechanics, biomechanics, computational biology, multibody system dynamics, and. Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. Johnson, contact mechanics, 1985, cambridge university press. We would like to show you a description here but the site wont allow us. Large elastic deformations abebooks shop for books. The examples have been selected to provide progression in terms of complexity of problem and to illustrate the logical way in which the solution to a difficult problem can be developed. Mechanics of finite deformation and fracture crc press book. Aug 08, 2018 this paper examines the sizedependent fracture of a piezoelectric double cantilever beam dcb specimen based on large deformationstrain gradient theory. In what you describe, the material behaves linearly elastically, but the geometrical effect is nonlinear. Two types of friction conditions between the membrane and the substrate are considered. In each of these theories the strain is then defined differently. We study the large deformation mechanics of contact and adhesion between an inflated hyperelastic membrane and a rigid substrate. Development and implementation of robust large deformation. In this work, we employ the hybrid finite element methodology along with the mortar method towards.
Computational contact mechanics peter wriggers springer. The approach includes a continuum contact mechanics model combined with an augmented lagrangian method for treating the contact and friction inequality. Autoclave processing of large scale, onepiece structural parts made of carbon fiberreinforced polymer composite materials is the key to decreasing manufacturing costs while at the same time increasing quality. In this technical note, the effect of large deformation on the contact of an axisymmetric circular plate that rests unilaterally on an elastic foundation is investigated. Reflecting two decades of research and development by the author and his group at the institute of computer applications ica, stuttgart university, this volume explores the computer simulation of large deformation processes. Direct measurements of the local membrane apex strain during noncontact inflation indicated that the neohookean model provides an accurate measure of membrane strain and supports its use as the. In addition, each chapter concludes with an extensive. In addition, the book covers the fracture phenomena in brittle or quasibrittle materials in which large deformation does not occur. A large deformation frictionless contact treatment in nurbs. As knowledge of the progressive failure mechanism increases, it is now necessary to. Solid mechanics equations are usually formulated by tracking a certain volume of material as it translates, rotates, and deforms. A large deformation contact formulation is subsequently developed and tested in the frictional setting, where collocation confirms the excellent performance already obtained for the frictionless case. As an admirer and connoisseur of his work, i has a great joy when discovering the publication of his book nonlinear solid mechanics, which of course, soon joined my personal library. Mortar finite element methods for large deformation contact.
Jul 14, 2011 nurbsbased isogeometric analysis is applied to 3d frictionless large deformation contact problems. Nonsmooth surfaces soft and hard materials fastmoving impact large deformation contact parameters that can be customised contact stiffness. This section details the quasistatic implicit finite deformation elastoplastic material point method based on a total lagrangian formulation defined by the following weak statement of equilibrium 10. This treatise is concerned with the stresses and deformation of solid bodies in contact with each other. This barcode number lets you verify that youre getting exactly the right version or edition of a book. Even though the derivation of the theory is relatively difficult, the final solution is a set of simple analytical equations relating the properties of the system to the developed stress. Nurbsbased isogeometric analysis is applied to 3d frictionless large deformation contact problems. Nonetheless, even in manufacturing simple flat parts, residual strains and stresses are unavoidable. For structural design purposes and to aid in the assembly procedures, it is. It is associated with strain localization or shear banding and is also related to damage in material structures.
Theoretical basis article in computer methods in applied mechanics and engineering 19833. General framework for dynamic large deformation contact. Jul 02, 2018 several finite deformation, large sliding examples are illustrated below to verify the accuracy of the implementation and demonstrate the ability of the algorithm to accurately handle complex contact problems with a conceptually simple framework. In addition to the classical nonlinear continuum mechanics kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. Computational continuum mechanics wiley online books. A contact domain method for large deformation frictional contact problems. This item is printed on demand print on demand neuware in this book, a theoretical analysis is presented for estimating the 3d large displacement elastic stability behavior including shear deformations of both ordinary and cableframe interactions in their both suspended or stayed cases subjected to. Large deformation contact mechanics of long rectangular membranes.
This paper examines the sizedependent fracture of a piezoelectric double cantilever beam dcb specimen based on large deformationstrain gradient theory. For the term s use in engineering, see deformation engineering. Tribology and contact mechanics books tribology tribonet. Contact mechanicsthe quantitative study of the stresses and deformation at the. This book is extremely well illustrated with a large numberof highquality line diagrams, tables and graphs, and the odd photograph. A large deformation frictionless contact treatment in. Deformationbased processing of materials 1st edition. Implicit in this condition is the assumption that the contact. It is suspended at a distance of d above a rigid flat substrate and is clamped at the edges o 1 and o 2.
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