time integration algorithm

TThe proposal and development of time integration algorithms in hyperelastic-based plasticity or hyperelastoplasticity, are consistently required due to complex issues such as objectivity. Through the multiplicative decomposition of the deformation gradient tensor, a local configuration known as the intermediate or plastic configuration is generated alongside the reference and the current configurations. Utilizing the intermediate configuration for time integrations eliminates the need to analyze the impact of rigid rotations in the current configuration. Moreover, as the Cauchy stress is derived from parameters in the intermediate configuration, there is no necessity to assess its objectivity. By employing the multiplicative decomposition of the gradient tensor of plastic deformation, equations for kinematic hardening can be derived, eliminating the need to verify objectivity. Therefore, in this article, the algorithm for the subloading surface model, based on the intermediate configuration, is derived by adapting the von Mises model. The rationale behind employing the von Mises model lies in its simplicity compared to the subloading surface model, along with its widespread usage. Additionally, in numerical implementation, the subloading surface model is more complex than the von Mises model. Building upon this, the problem of simple shear deformation with small and large elastic strains, incorporating isotropic, kinematic, and combined hardening in plasticity, has been investigated. The obtained results have been compared with the experimental data and findings from various references. The comparison between the results presented in this article and the available data indicates agreement, suggesting the viability of employing this model in practical applications.