A Thermodynamically Consistent Anisotropic Continuum Damage Mechanics Model With Damage-Dependent Equivalent Strain

Abstract This paper proposes a new thermodynamically consistent anisotropic continuum damage mechanics model that the degradation of material is described by a set of damage variables. We adopt a set of novel equivalent strains which are functions of both the strain and the damage state variables as well. A viscous stabilization method is considered to improve the convergence during the material softening. The evolution of damage state variables is updated through a Newton–Raphson iterative process. The expression of the consistent tangent stiffness matrix is also derived. A smoothed exponential damage evolution shape function with rescaling regularization method is proposed to describe the material softening process and the mesh dependency phenomenon is relieved. Several sets of numerical examples including three-point-bending of a notched beam, uniaxial tension of unnotched and notched plate of composite material with multiple layups are presented to verify the anisotropic damage models.