Section 2.1 - Introduction to Elasticity and Viscoelasticity

Abstract

This chapter provides a brief introduction on elasticity and viscoelasticity. For all solid materials there is a domain in stress space in which strains are reversible due to small relative movements of atoms. For many materials like metals, ceramics, concrete, wood, and polymers, in a small range of strains, the hypotheses of isotropy and linearity are good enough for many engineering purposes. Then the classical Hooke's law of elasticity applies. It can be derived from a quadratic form of the state potential, depending on two parameters characteristics of each material: the Young's modulus and the Poisson's ratio. Viscoelasticity considers a dissipative phenomenon due to "internal friction," such as between molecules in polymers or between cells in wood. Isotropy, linearity, and small strains allow for simple models. Quadratric functions for the state potential and the dissipative potential lead to either Kelvin-Voigt or Maxwell's models, depending upon the partition of stress or strains in a reversible part and in an irreversible part. They are described in three dimensions. Kelvin-Voigt model: Maxwell model.