Numeric modeling of forced multistage growth of a hole in elastoplastic solid under superimposed large strains

V. A. Levin   ; K. M. Zingerman   ; M. A. Kartsev

Čebyševskij sbornik, Tome 25 (2024) no. 4, pp. 228-238

Résumé

The stress-strain state in the vicinity of a cavity formed in a pre-strained body made of elastic-plastic material is calculated for the case of step-by-step cavity growth in several stages. The problem is solved in a quasi-static formulation for finite strains taking into account their redistribution after each stage of deformation. It is assumed that the transition of material to a plastic state occurs in accordance with the von Mises plasticity condition, and plastic deformation of the material is described by the associated law of plastic flow. The problem is formulated and solved based on the theory of multiple superposition of large strains. A general algorithm for solving the problem within the framework of this theory is presented. The finite element method and the spectral element method are used for the solution. The methods and algorithms implemented in the Fidesys engineering strength analysis system and software modules included in this system were used in the solution. Model calculations are performed for the case of plane deformation of a square body with a central elliptical (at the time of formation) cavity, the growth of which occurs in several stages according to a predetermined law. Graphs of stress distribution in the body are given. The influence of plastic properties of the material and multi-stage deformation on the stress-strain state is investigated.

Détail

Keywords: forced growth of defect, multi-stage deformation, multiple imposition of large deformations, elastic-plastic material, plane deformation, finite element method, spectral element method.