Finite deformation elasticity theory

Merodio, J. and Ogden, R. (2020) Finite deformation elasticity theory. In: Merodio, J. and Ogden, R. (eds.) Constitutive Modelling of Solid Continua. Series: Solid mechanics and its applications (262). Springer: Cham, pp. 17-52. ISBN 9783030315467 (doi:10.1007/978-3-030-31547-4_2)

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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.

Item Type:Book Sections
Status:Published
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Merodio, J., and Ogden, R.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Publisher:Springer
ISBN:9783030315467
Published Online:14 November 2019

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