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
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.
scientific article; zbMATH DE number 1569554