Advances in Constitutive Relations Applied in Computer Codes (CISM International Centre for Mechanical Sciences)

~ SpringerWienNewYork CISM COURSES AND LECTURES Series Editors: The Rectors Giulio Maier - Milan Jean Salençon - Pal...

Author: Janusz R. Klepaczko | Tomasz Lodygowski

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~ SpringerWienNewYork

CISM COURSES AND LECTURES

Series Editors: The Rectors Giulio Maier - Milan Jean Salençon - Palaiseau Wilhelm Schneider - Wien

The Secretary General Bernhard Schrefler - Padua

Executive Editor Paolo Serafini - Udine

The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.

INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES - No. 515

ADVANCES IN CONSTITUTIVE RELATIONS APPLIED IN COMPUTER CODES

EDITED BY JANUSZ R. KLEPACZKO UNIVERSITÈ DE METZ, METZ CEDEX, FRANCE TOMASZ ŁODYGOWSKI POZNAN UNIVERSITY OF TECHNOLOGY, POZNAN, POLAND

This volume contains 158 illustrations

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 2009 by CISM, Udine Printed in Italy SPIN 12754533

All contributions have been typeset by the authors.

ISBN 978-3-211-99708-6 SpringerWienNewYork

PREFACE Many important industrial applications incline toward better understanding of the constitutive properties of matter. Nowadays, the development of measurement possibilities, even in nanoscale, allows for multiscale formulations that drive to the more sophisticated models used in continuum mechanics. These phenomenological models are particularly important and useful for solutions of very concrete initial boundary value problems. Our interests are focused mainly on detailed descriptions of material behavior that depend not only on simple stress-strain relationships but also includes the strong influence of loading type, which introduces temperature, strain rate dependence, fracture, etc. Understanding these physics phenomena is of fundamental importance for successful and responsible computations. In particular, using the popular commercial programs requires deep understanding of constitutive formulations and their restrictions. These lectures are addressed to industrial users who are responsible for making crucial decisions in design, as well as, to young scientists who work on new models that describe the behavior of materials which also account the new influences and reflect the complexity of the material behavior. At the end, let me express my gratitude to the lecturers of the CISM course No. 328 on “Advances in Constitutive Relations Applied in Computer Codes”, held in Udine in July 2007, who finally prepared the included materials. Unfortunately, during the preparation and collecting papers for this book, our friend and colleague Prof. Janusz R. Klepaczko passed away. This is a very big loss for the society of mechanics. Prof. J.R.Klepaczko was the initiator of this course and the editor of this material. We dedicate this book to His memory. Tomasz Lodygowski

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CONTENTS

Preface Tomasz Lodygowski Preface Janusz R. Klepaczko Constitutive Relations in Dynamic Plasticity, Pure Metals and Alloys by Janusz R. Klepaczko .................................................... 1 Modeling of Rubberlike Materials by A. Luis Dorfmann .................................................... 147 Imperfect Bonding with Nonpenetration Condition by George Mejak ........................................................... 203 Selected Constitutive Relations in Practical Computations by Tomasz Łodygowski .................................................. 261

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Stress

0.15 0.125 0.1 0.075 0.05 0.025

60 50 40 30 20 10 0

0.2 0.4 0.6 0.8 1 1.2 1.4 Strain

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1.2 1.4

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0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02

Debonded area

Stress


257

70 60 50 40 30 20 10 0

0.2 0.4 0.6 0.8 1 1.2 1.4 Strain

0.2 0.4 0.6 0.8 1 Strain

1.2 1.4

Debonded area

Young modulus

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262

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