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Published in:
2013 | OriginalPaper | Chapter
2. Fundamentals of Linear Elasticity
Authors : Reza Eslami, Richard B. Hetnarski, Jozef Ignaczak, Naotake Noda, Naobumi Sumi, Yoshinobu Tanigawa
Published in: Theory of Elasticity and Thermal Stresses
Publisher: Springer Netherlands
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Abstract
In this chapter a number of concepts are introduced to describe a linear elastic body. In particular, the displacement vector, strain tensor, and stress tensor fields are introduced to define a linear elastic body which satisfies the strain-displacement relations, the equations of motion, and the constitutive relations. Also, the compatibility relations, the general solutions of elastostatics, and an alternative definition of the displacement field of elastodynamics are discussed. The stored energy of an elastic body, the positive definiteness and strong ellipticity of the elasticity fourth-order tensor, and the stress-strain-temperature relations for a thermoelastic body are also discussed.