Logarithmic stress rate based constitutive model for cyclic loading in finite plasticity

• A cyclic finite plastic constitutive model is constructed.
• A logarithmic stress rate is employed in the proposed model.
• The Ohno–Abdel–Karim kinematic hardening rule is extended for finite plasticity.
• The proposed model is implemented into a finite element code, ABAQUS.
• Cyclic deformations of materials in the range of finite strain are predicted well.

Based on the logarithmic stress rate, a constitutive model is developed to describe the material behaviour under cyclic loading histories (including ratchetting) in the framework of finite plasticity by using combined nonlinear isotropic and kinematic hardening rules. The nonlinear kinematic hardening rule is extended from that developed by Abdel-Karim and Ohno (2000) for infinitesimal plasticity. The cyclic hardening/softening feature of materials is reflected by using a nonlinear isotropic hardening rule. Then, the proposed model is implemented into a finite element code (e.g., ABAQUS) by employing a simple fully-implicit time-integration procedure. Finally, some numerical examples are carried out to verify the capability of the model to predict the cyclic deformation of materials in finite deformation by comparing the predictions with the corresponding experiment results in referable literature. The predicted stress responses during a simple shear with large shear strain and ratchetting during the cyclic loading tests in finite deformation are in good agreement with the corresponding experimental results.