On the formulation of anisotropic elastic degradation. I: Theory based on a pseudo-logarithmic damage tensor rate. II: Generalized pseudo-Rankine model for tensile damage
type: Item
instance of: scholarly article
title: On the formulation of anisotropic elastic degradation. I: Theory based on a pseudo-logarithmic damage tensor rate. II: Generalized pseudo-Rankine model for tensile damage
zbMATH Open document ID: 1006.74007
DOI: 10.1016/S0020-7683(00)00030-5
author: Ignacio Carol
author: Egidio Rizzi
author: Kaspar Willam
published in: International Journal of Solids and Structures
publication date: 2003-03-12T00:00:00Z
review text: In order to derive general evolution laws, the authors resort to the definition of a conjugate force of damage. Based upon a loading function and a damage rule with physical meaning, the authors define this force as a factor multiplying the compliance rate occurring in the expression for dissipation energy rate. The further introduced pseudo-logarithmic damage tensor rate leads to a convenient separation of volumetric and deviatoric tensorial parts, responsible respectively for isotropic and deviatoric degradations. The authors use an elastic degradation and damage theory with a second-order tensor (secant) formulation which allows to establish simplified micro- and macro-models for degradation. The damage scalar is linked with the introduced tensors, and an additional calculation provides explicite formulas for introduced measures. In part II, the results of part I are applied in order to develop a generalized model by formulating the loading function as a particular function of the conjugate damage force and history function. The shape of the loading surface in stress space is obtained together with a damage rule and hardening/softening laws. In the case of uniaxial tension and in other simple loading cases (pure shear, pure distortion, tensile loading), the constitutive laws are obtained in closed form. A numerical test with rotation of principal axes is performed, and plotted diagrams illustrate each analyzed case. We also mention the illustration of loading paths and frictional criteria in diagrams and tables.
reviewed by: M. Mişicu
Mathematics Subject Classification ID: 74A45
Mathematics Subject Classification ID: 74R20
zbMATH DE Number: 1569554
zbMATH Keywords: anisotropic elastic degradation
zbMATH Keywords: generalized pseudo-Rankine model
zbMATH Keywords: tensile damage
zbMATH Keywords: fracture cracking
zbMATH Keywords: conjugate force of damage
zbMATH Keywords: loading function
zbMATH Keywords: damage rule
zbMATH Keywords: dissipation energy rate
zbMATH Keywords: pseudo-logarithmic damage tensor rate
zbMATH Keywords: uniaxial tension
MaRDI profile type: Publication
Wikidata QID: Q126643395
description: scientific article; zbMATH DE number 1569554