The fully implicit backward Euler scheme is developed for this model to be solved in a Newton–Raphson solution procedure. However, in addition to that the coupling is further enhanced through the use of the functional forms of the hardening variables introduced in this formulation.The use of this formulation in solving boundary value problems will be presented in future work. The proposed work introduces a strong coupling between damage and plasticity by utilizing damage and plasticity flow rules that are dependent on both the plastic and damage potentials.
however, it does not address the relevant appropriateness of certain forms to solve different problems.
The paper discusses the general concept of using such functional forms. Various exponential and power law functional forms are studied in this formulation. The hardening conjugate forces (stress-like terms) are general nonlinear functions of their corresponding hardening state variables (strain-like terms) and can be defined based on the desired material behavior. Additionally, a damage isotropic hardening is incorporated as a state variable to describe the change of the damage surface. Isotropic hardening and kinematic hardening are incorporated as state variables to describe the change of the yield surface. In deriving the constitutive model, a local yield surface is used to determine the occurrence of plasticity and a local damage surface is used to determine the occurrence of damage. The damage is introduced through a damage mechanics framework and utilizes an anisotropic damage measure to quantify the reduction of the material stiffness.
The formulation of the elasto-plastic-damage behavior of materials is introduced here within a framework that uses functional forms of hardening internal state variables in both damage and plasticity. This work gives the thermodynamically consistent theoretical formulations and the numerical implementation of a plasticity model fully coupled with damage.
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