Localization properties of Desmorat's anisotropic damage model

This paper presents a systematic analysis of localization properties of the anisotropic damage model proposed by Desmorat and coworkers. The general localization condition, based on the vanishing determinant of the second-order localization tensor, is converted into a specific criterion valid for the present model and dependent on the current state variables and model parameters. The localization properties are then described in terms of (i) the critical value of a parameter governing the damage growth, (ii) the critical ratio between the tangent and elastic moduli, (iii) the direction of a potential weak discontinuity plane and (iv) the discontinuity mode. For plane-stress and plane-strain states, these characteristics are investigated in detail and the differences between two- and three-dimensional analyses are explained and discussed. The theoretical results are verified by numerical simulations of a bar under uniform tension using a skewed finite element mesh, which allows localization into inclined bands of different directions.