Method and software for finite element solution of two-dimensional creep problems at large deformations

Abstract

The paper presents the formulation of a two-dimensional problem of the creep theory for the case of finite strains. A description of the foundations of the calculation method presents. The method is based on the use of the generalized Lagrange-Euler (ALE) approach, in which the boundary value problem in the current solid configuration is solved by using FEM. A triangular element is involved in the numerical modeling. At each stage of creep calculations in the current configuration, the initial problem is solved numerically using the finite difference method. The preprocessing data preparation is carried out in the homemade RD program, in which two-dimensional model is surrounded by a mesh of special elements. This feature implements the ALE algorithm for the motion of material elements along the model. The examples of preprocessing as well as of the mesh rebuilding in the case of finite elements transition are given. Creep calculations are performed in the developed program, which is based on the use of the FEM Creep software package in the case of finite strains. The regular mesh is used for calculations, which allow us to use the efficient algorithm for transition between current configurations. The numerical results of the creep of specimens made from aluminum alloys are compared with the experimental and calculated ones obtained by integrating the constitutive equations. It was concluded that for material with ductile type of fracture the presented method and software allow to obtain results very close to experimental only by use of creep rate equation. Creep simulations of material with mixed brittle-ductile fracture type demand use the additional equation for damage variable.