Computational efficiency of explicit integration schemes in crystal plasticity

This project is based on the study of computational efficiency in crystal plasticity, so first, as an introduction, aspects that help to understand and serve as preliminary knowledge of crystal plasticity are discussed. Issues related to the atomic arrangement of the materials, in what forms they can be arranged, what structures they can form and what defects they present, among other concepts, are explained. Next, it is necessary to define aspects of the solid mechanics theory, which are the basis for the calculations to be carried out in this project. The kinematics of continuous bodies, equilibrium and the constitutive equations are discussed. The role of numerical integration methods and the two main methods to consider in this project are also introduced. In order to put the above knowledge into practice, a simple one-dimensional shear case is studied and the corresponding comparison between the different numerical integration methods is carried out in order to determine their computational efficiency. Finally, a simple two-dimensional elastoplastic shear case is implemented by means of the analysis of the finite element method (FEM) with the different explicit integration schemes and results and conclusions are obtained from all the procedures carried ou