Oriented damage in ductile sheets: Constitutive modeling and numerical integration

Thermodynamics with internal variables provides a framework for constitutive modeling of elasto-plastic deformations. Within the scope of the theory, constitutive and evolution equations for ductile, elasto-plastic materials with mixed (isotropic and kinematic) hardening and anisotropic damage have been developed. Postulates within continuum damage mechanics were used in order to incorporate damage as an internal variable. Owing to this, and to a simplified definition of the inverted damage effect tensor, a general expression for degradation of the elastic properties in materials has been obtained. The corresponding numerical algorithm for integration of the constitutive equations is based on an elastic predictor - plastic/ damage corrector procedure. The plastic/damage corrector is uncoupled, which further simplifies and expedites the corrector procedure