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Strongly Orthotropic Continuum Mechanics

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Strongly Orthotropic Continuum Mechanics A theory of Strongly orthotropic continuum mechanics D.C. Kellermann A dissertation presented for the degree of Doctor of Philosophy June 2008 School of Mechanical and Manufacturing Engineering, J17, The University of New South Wales, Sydney, NSW 2052, Australia ABSTRACT The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Imple- mentable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectiv- ity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Corotation and P–I–C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame gener- ates previously unreported results in strongly orthotropic continua. Dedicated to you, dad. [Bill Kellermann, 1942–2006] … if only you’d have seen me finish. ACKNOWLEDGEMENTS Dr. Tomonari Furukawa From whom I’ve unquestionably learnt the most. Prof. Don Kelly Thank you, Don, for being a great mentor to me. CMR Group and all my colleagues Especially to Mike and Hin, for the thousand-odd discussions and the thousand-odd cups of cof- fee. To Amm of course, Ian, Daniel, Ben, Pan, Stephen, Ryan, Alex, Edward, Phil, Mark, Daud, Baneen, Luke, Zoltan, Garth and whoever else might have listened while I harangued. My family To Eva (mum), for the endless support. To my oldest brother Adam, to Ann-Maree and Marissa, but particularly to my brother Mike who seems astoundingly to have become quite familiar with the fields of continuum and computational mechanics. My good friends To Dr. Tim O’Neill for being a role model of sorts, to Mike Forward for being my best mate for so many years, and to Richard Urwin for a genuinely motivating—and often humorous— interest and enthusiasm in my work. Also thanks to Ed Giles and others for their ongoing and much-appreciated encouragement. The Cooperative Research Centre for Advanced Composite Structures The support given by individuals associated with the CRC-ACS is gratefully acknowledged, including Xiaobo Yu, Damian McGuckin, Rowan Paton, Michael Bannister, Israel Herszberg and Murray Scott. iv ORIGINALITY STATEMENT ‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowl- edgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’ Signed ………………………………………………….. Date ………………...…… v COPYRIGHT STATEMENT ‘I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have ap- plied/will apply for a partial restriction of the digital copy of my thesis or dissertation.' Signed ………………………………………………….. Date ………………...…… AUTHENTICITY STATEMENT ‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital for- mat.’ Signed ………………………………………………….. Date ………………...… vi CONTENTS ABSTRACT ...................................................................................................................... 2 ACKNOWLEDGEMENTS ............................................................................................. iv ORIGINALITY STATEMENT ........................................................................................ v COPYRIGHT STATEMENT .......................................................................................... vi AUTHENTICITY STATEMENT ................................................................................... vi CONTENTS ................................................................................................................... vii LIST OF FIGURES ........................................................................................................ xii LIST OF TABLES ......................................................................................................... xvi ABBREVIATIONS ...................................................................................................... xvii Chapter 1 ........................................................................................................................... 1 Introduction ....................................................................................................................... 1 1.1 An introduction to strongly orthotropic continuum mechanics ............................... 1 1.1.1 A brief appraisal of continuum mechanics from its inception........................... 2 1.1.2 Evidence for change .......................................................................................... 4 1.1.3 Why strongly orthotropic continuum mechanics? ............................................. 5 1.2 Objective .................................................................................................................. 7 1.3 Approach .................................................................................................................. 7 1.4 Principal technical contributions ............................................................................. 9 1.5 Publications and presented work ............................................................................. 9 1.6 Organisation ........................................................................................................... 10 1.7 Disambiguation ...................................................................................................... 12 1.7.1 Notational categorisations ............................................................................... 12 1.7.2 Definitions ....................................................................................................... 12 1.7.3 Footnotes ......................................................................................................... 12 Chapter 2 ......................................................................................................................... 13 Literature review ............................................................................................................. 13 vii viii 2.1 Kinematically driven models for fibre-reinforced materials ................................. 13 2.2 FE-implementable constitutive models for composites ......................................... 15 2.3 Experimental techniques for finite deformation of CFRPs ................................... 17 2.4 Specialised continuum approaches for strong orthotropy ...................................... 20 2.5 Some relevant micropolar and Cosserat theory ..................................................... 23 2.6 Finite element techniques for behavioural compensation ...................................... 25 2.7 Multi-scale and experimental mapping approaches ............................................... 26 2.8 Chapter summary ................................................................................................... 28 Chapter 3 ......................................................................................................................... 29 Strongly orthotropic continuum mechanics .................................................................... 29 3.1 Mechanics of orthotropic materials ....................................................................... 29 3.1.1 The linear tensors of the displacement state .................................................... 29 3.1.2 Strongly orthotropic kinematics and deformation
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