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2012 | OriginalPaper | Chapter

5. Inelastic Constitutive Equation and Damage Evolution Equation of Material with Anisotropic Damage

Author : Sumio Murakami

Published in: Continuum Damage Mechanics

Publisher: Springer Netherlands

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Abstract

The development of microvoids in materials usually depends on the direction of the applied stress, and hence the material damage is essentially anisotropic. In this chapter we consider the damage mechanics theories of the constitutive and the evolution equations of materials with anisotropic damage.

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previous chapter Inelastic Constitutive Equation and Damage Evolution Equation of Material with Isotropic Damage

next chapter Elastic-Plastic Damage

As regards the formulation taking account of the kinematic hardening, refer to Besson et al. (2010).

According to the definition (3.26), the Gibbs potential Γ is usually a negative-valued function.

Since the description of (1) and (2) in this Subsection is applicable also to damage tensor \(\boldsymbol{\mathcal{D}}\) of an arbitrary even-order, the elastic modulus tensor in damaged state will be denoted here by \({\mathbb C}(\boldsymbol{\mathcal{D}})\) with the argument \(\boldsymbol{\mathcal{D}}\).

Besson J, Cailletaud G, Chaboche J-L, Forest S, Blétry M (2010) Non-linear mechanics of materials. Springer, Dordrecht

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Title: Inelastic Constitutive Equation and Damage Evolution Equation of Material with Anisotropic Damage
Author: Sumio Murakami
Publisher: Springer Netherlands
Book: Continuum Damage Mechanics
Print ISBN: 978-94-007-2665-9

Electronic ISBN: 978-94-007-2666-6

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-94-007-2666-6_5

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