generalized trapezoidal algorithm

In this paper, a general elastoplastic-damage constitutive model considering the effect of strain rate has been developed. The derivation of this model has been cast into the irreversible thermodynamics with internal variables within the fundamentals of Continuum Damage Mechanics (CDM). The rate effect has been involved as an additional term into the plastic yield surface (dynamic plastic yield surface). Therefore, the plastic surface has been presented in the category of Consistency–type model in which the rate of state variables is considered as independent state variables. The damage has been assumed as a tensor type variable and based on the energy equivalence hypothesis the damage evolution has been developed. The proposed model has been validated for both rate-independent and rate-dependent deformation. For this manner, the generalized trapezoidal stress integration algorithm of the model has been explained and the model has been implemented into user-defined subroutines (UMAT and VUMAT) in the finite element program ABAQUS. The results of numerical simulation, statically and dynamically, have been compared to the experimental results of three aluminum and two steel alloys. Also, the results of simulation for shear and double-notched tests have been compared to their experiments. By comparing the predicted results with experimental data, the capability and validity of the model have been verified.