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Finite Deformation Elasticity Theory

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Constitutive Modelling of Solid Continua

Part of the book series: Solid Mechanics and Its Applications ((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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Author information

Authors and Affiliations

  1. Department of Continuum Mechanics and Structures, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    José Merodio

  2. School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow, G12 8SQ, UK

    Raymond Ogden

Authors
  1. José Merodio
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  2. Raymond Ogden
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Corresponding author

Correspondence to José Merodio .

Editor information

Editors and Affiliations

  1. Department of Continuum Mechanics and Structures, Escuela de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Madrid, Spain

    José Merodio

  2. School of Mathematics and Statistics, University of Glasgow, Glasgow, UK

    Raymond Ogden

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Merodio, J., Ogden, R. (2020). Finite Deformation Elasticity Theory. In: Merodio, J., Ogden, R. (eds) Constitutive Modelling of Solid Continua. Solid Mechanics and Its Applications, vol 262. Springer, Cham. https://doi.org/10.1007/978-3-030-31547-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-31547-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31546-7

  • Online ISBN: 978-3-030-31547-4

  • eBook Packages: EngineeringEngineering (R0)

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