Advanced Methods of Continuum Mechanics for Materials and Structures by Konstantin Naumenko & Marcus Aßmus

Author:Konstantin Naumenko & Marcus Aßmus
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

2 Nonlocal and Gradient-Enhanced Damage Models

In this section, a concise overview will be given of damage models, including the nonlocal and gradient-enhanced extensions, and a numerical example will be given of broadening of the damage zone.

2.1 Damage Models

Herein, we restrict ourselves to an isotropic damage evolution. Assuming that Poisson’s ratio remains constant during the damage process, the following total stress–strain relation is obtained:

(1)

with d a scalar damage variable which grows from zero to one (at complete loss of integrity) and the fourth-order elastic stiffness tensor. For strain-based damage models, the total stress–strain relation, Eq. (1), is complemented by a damage-loading function

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