Numerical aspects of non-local modeling of the damage evolution in elastic–plastic materials

Abstract The design of mechanical systems in modern industrial plants requires reliable and efficient methods to predict the behavior of structural materials. For complex loading conditions, the behavior of the structural materials is determined by damage evolution, strain rate and temperature. The subject of the article is the modeling of the damage evolution in elastic–plastic materials of structural components, which are utilized at various temperatures. To achieve this goal, a hybrid model of steel cracking is applied. The hybrid model uses a finite element simulation combined with an experimental test realized in the macroscale. By using the hybrid model, the modeling of the damage evolution affords possibilities of determining macroscopic effects of the steel micro-defects. An essence of solving the predicting behavior of structural materials with micro-defects consists in time integration procedures for constitutive equations. In the article a semi-implicit time integration procedure is presented. The semi-implicit time integration procedure is suitable for the inelastic materials (compressible or incompressible) with the combined kinematic–isotropic hardening behavior. Its numerical solutions are stable, namely without the oscillatory behavior. By spatial averaging over a representative volume (RV), the homogenization technique (HT) is used for the defining of non-local variables in the constitutive equations. Evolutionary algorithms (EAs) based on local selections are applied to perform the homogenization technique. Within the framework of the large strain theory, the non-local continuum satisfies the objectivity requirements. Limitations on applicability of the J -integral approach to construct crack growth resistance curves are also presented.