Design of Polyconvex Energy Functions for All Anisotropy Classes PDF Download

Author: Vera Ebbing
Publisher:
ISBN: 9783980967945
Category :
Languages : en
Pages : 206

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Author: Jörg Schröder
Publisher: Springer
ISBN: 3319319256
Category : Mathematics
Languages : en
Pages : 239

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Book Description
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.

Author: Yuriy I. Dimitrienko
Publisher: Springer Science & Business Media
ISBN: 9400700342
Category : Science
Languages : en
Pages : 742

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Book Description
The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Author: Georges Limbert
Publisher: Springer
ISBN: 303013279X
Category : Technology & Engineering
Languages : en
Pages : 303

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This book presents state-of-the-art experimental and modelling techniques for skin biophysics that are currently used in academic and industrial research. It also identifies current and future challenges, as well as a growing number of opportunities in this exciting research field. The book covers the basics of skin physiology, biology, microstructural and material properties, and progressively introduces the reader to established experimental characterisation protocols and modelling approaches. Advanced topics in modelling theories and numerical implementation are also presented. The book focusses especially on: 1. Basic physiology, molecular biology, microstructural and material properties of the skin. 2. Experimental characterisation techniques for the skin (including imaging): in vivo and in vitro techniques and combination of those with in silico approaches. 3. State-of-the-art constitutive models of the skin: elastic, anelastic and mechanobiological formulations (e.g. growth, ageing, healing). 4. Applications: mechanics, damage, biological growth, healing, ageing and skin tribology. This book is addressed to postgraduate students in biomedical/mechanical/civil engineering, (bio)physics and applied mathematics, postdoctoral researchers, as well as scientists and engineers working in academia and industry engaged in skin research, particularly, if at the cross-roads of physical experiments, imaging and modelling. The book is also be of interest to clinicians/biologists who wish to learn about the possibilities offered by modern engineering techniques for skin science research and, by so doing, provide them with an incentive to broaden their outlook, engage more widely with the non-clinical research communities and, ultimately, help cross-fertilising new ideas that will lead to better treatment plans and engineering solutions.

Author: David J. Steigmann
Publisher: Oxford University Press
ISBN: 0192528076
Category : Mathematics
Languages : en
Pages : 175

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Containing case studies and examples, the book aims to cover extensive research particularly on surface stress and topics related to the variational approach to the subject, and non-standard topics such as the rigorous treatment of constraints and a full discussion of algebraic inequalities associated with realistic material behaviour, and their implications. Serving as an introduction to the basic elements of Finite Elasticity, this textbook is the cornerstone for any graduate-level on the topic, while also providing a template for a host of theories in Solid Mechanics.

Author: Jörg Schröder
Publisher: Springer Science & Business Media
ISBN: 3709101743
Category : Technology & Engineering
Languages : en
Pages : 361

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Book Description
Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Author: Stefan Kollmannsberger
Publisher: Springer Nature
ISBN: 3030765873
Category : Technology & Engineering
Languages : en
Pages : 108

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Book Description
This book provides a first course on deep learning in computational mechanics. The book starts with a short introduction to machine learning’s fundamental concepts before neural networks are explained thoroughly. It then provides an overview of current topics in physics and engineering, setting the stage for the book’s main topics: physics-informed neural networks and the deep energy method. The idea of the book is to provide the basic concepts in a mathematically sound manner and yet to stay as simple as possible. To achieve this goal, mostly one-dimensional examples are investigated, such as approximating functions by neural networks or the simulation of the temperature’s evolution in a one-dimensional bar. Each chapter contains examples and exercises which are either solved analytically or in PyTorch, an open-source machine learning framework for python.

Author: Peter Wriggers
Publisher: Springer Science & Business Media
ISBN: 3211772987
Category : Science
Languages : en
Pages : 252

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Book Description
Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1852

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Author: Morton E. Gurtin
Publisher: Cambridge University Press
ISBN: 1139482157
Category : Science
Languages : en
Pages : 721

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Book Description
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.