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Finite Deformation Elasticity Theory

  • José MerodioEmail author
  • Raymond Ogden
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 262)

Abstract

This chapter provides the framework for the development of constitutive theories of solids by focusing on constitutive laws for nonlinearly elastic solids. These exemplify the general principles of constitutive theory that should be applied to all types of material behaviour, in particular, the notions of objectivity and material symmetry, including the important symmetries of isotropy, transverse isotropy and orthotropy based in part on deformation invariants. Details are given for the various general stress–deformation relations for each case of symmetry in respect of hyperelastic materials (which are characterized by a strain-energy function), with or without an internal constraint such as incompressibility, and these are illustrated by particular prototype models. The notion of residual stress (in an unloaded configuration) is discussed and the form of strain-energy function required to accommodate residual stress in the material response is developed.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Continuum Mechanics and Structures, Escuela de Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

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