Viscoelastic Modeling for Structural Analysis

Jean Salençon

• Publisher: Wiley-ISTE
• Year: 2019
• Print ISBN: 9781786304452
• eBook ISBN: 9781119618355
• Edition: 1
• Topic: Technologie et ingénierie
• Subtopic: Science des matériaux

The theory of viscoelasticity has been built up as a mechanical framework for modeling important aspects of the delayed behavior of a wide range of materials. This book, primarily intended for civil and mechanical engineering students, is devoted specifically to linear viscoelastic behavior within the small perturbation framework. The fundamental concepts of viscoelastic behavior are first presented from the phenomenological viewpoint of the basic creep and relaxation tests within the simple one-dimensional framework. The linearity and non-ageing hypotheses are introduced successively, with the corresponding expressions of the constitutive law in the form of Boltzmann's integral operators and Riemann's convolution products respectively. Applications to simple quasi-static processes underline the dramatic and potentially catastrophic consequences of not taking viscoelastic delayed behavior properly into account at the design stage. Within the three-dimensional continuum framework, the linear viscoelastic constitutive equation is written using compact mathematical notations and takes material symmetries into account. The general analysis of quasi-static linear viscoelastic processes enhances similarities with, and differences from, their elastic counterparts. Simple typical case studies illustrate the importance of an in-depth physical understanding of the problem at hand prior to its mathematical analysis.

1
One-dimensional Viscoelastic Modeling

1.1. Experimental observations

Everyday practice, either domestic or industrial, provides examples of the delayed response of common materials to mechanical actions: the slow sagging of bookcase shelves subjected to the weight of knowledge, the progressive return¹ of a polymer sample to its initial configuration after being subjected to a temporary loading process and creep of concrete and asphalt are just a few examples of evidence of this kind of behavior. That being said, it is necessary to go into some detail regarding the timescales that are referred to when describing the above-mentioned phenomena: the qualifiers “slow” and “progressive” are used here with the meaning that the characteristic times of these phenomena are long when compared with the propagation time associated with the “instantaneous” response of the same material in the studied system.

Some consequences of these phenomena are just perceived as inconveniences either from an aesthetic viewpoint or regarding comfortable serviceability of a structure (e.g. an independent span bridge or similar isostatic structures). However, more damaging consequences may occur, such as delayed deformations that can be incompatible with the serviceability of a structure (a crane runway, for instance), and can even prove catastrophic when they generate, during the course of time, the redistribution of internal forces in a prestressed hyperstatic structure. On the otherx hand, bitumen, putties and polymers are used as dampers in industrial applications because of the dissipative effects caused by delayed deformations.

Clearly, the effect...

Table of contents

• Cover
• Table of Contents
• Preface
• List of Notations
• 1 One-dimensional Viscoelastic Modeling
• 2 Rheological Models
• 3 Typical Case Studies
• 4 Three-dimensional Linear Viscoelastic Modeling
• 5 Quasi-static Linear Viscoelastic Processes
• 6 Some Practical Problems
• Appendix
• References
• Index
• End User License Agreement