Book•
Non-Linear Elastic Deformations
01 Jan 1984-
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
Abstract: non linear elastic deformations iwsun non linear elastic deformations erpd non linear elastic deformations hneun non-linear elastic deformations (dover civil and non-linear elastic deformations of multi-phase fluid systems non linear elastic deformations dover civil and mechanical ogden nonlinear elastic deformations pdf wordpress non-linear, elastic researchgate chapter 6 non linear material models international journal of nonlinear mechanics nonlinear elastic deformations ogden pdfslibforme international journal of non-linear mechanics 1 rubber elasticity: basic concepts and behavior non linear elastic deformations dover civil and mechanical on a non-linear wave equation in elasticity non linear elastic deformations (pdf) by r. w. ogden (ebook) exact formulations of non-linear planar and spatial euler introduction to nonlinear analysis mit opencourseware manual for the calculation of elastic-plastic materials non linear elastic axisymmetric deformation of membranes types of analysis: linear static, linear dynamic and non fracture mechanics, damage and fatigue non linear fracture chapter 2 linear elasticity freie universität the influence of non-linear elastic systems on the a simple geometric model for elastic deformations
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TL;DR: In this paper, the authors developed a constitutive law for the description of the (passive) mechanical response of arterial tissue, where the artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia.
Abstract: In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.
2,887 citations
Cites background from "Non-Linear Elastic Deformations"
...This fundamental physical requirement in hyperelasticity ensures that undesirable material instabilities are precluded (for a general discussion of convexity in hyperelasticity the reader is referred to, for example, [42], Section 6, and [7])....
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17 Aug 2012
TL;DR: De Borst et al. as mentioned in this paper present a condensed version of the original book with a focus on non-linear finite element technology, including nonlinear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity.
Abstract: Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist Rene de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature.
2,568 citations
Book•
01 Jan 1989TL;DR: In this article, the authors propose a floating frame of reference formulation for large deformation problems in linear algebra, based on reference kinematics and finite element formulation for deformable bodies.
Abstract: 1. Introduction 2. Reference kinematics 3. Analytical techniques 4. Mechanics of deformable bodies 5. Floating frame of reference formulation 6. Finite element formulation 7. Large deformation problem Appendix: Linear algebra References Index.
2,125 citations
TL;DR: A structural continuum framework that is able to represent the dispersion of the collagen fibre orientation is developed and allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls.
Abstract: Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379–4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.
1,905 citations
Book•
28 Sep 1997TL;DR: Bonet and Wood as discussed by the authors provide a complete, clear, and unified treatment of nonlinear continuum analysis and finite element techniques under one roof, providing an essential resource for postgraduates studying non-linear continuum mechanics and ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
Abstract: Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
1,859 citations