Serge Caperaa

Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis

A numerical implementation of the eXtended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms have been implemented, within an oriented object framework in C++, in the home made explicit FEM code. The new module, called DynaCrack, included in the dynamic FEM code DynELA, evaluates the crack geometry, the propagation of the crack and allow the post-processing of the numerical results. The module solves the system of discrete equations using an explicit integration scheme. Some numerical examples illustrating the main features and the computational efficiency of the DynaCrack module for dynamic crack propagation are presented in the last section of the paper.

Numerical propagation of dynamic cracks using X-FEM

This paper presents an application of the eXtended Finite Element Method for numerical modeling of the dynamic cracks propagation. The numerical cracks representation is adapted to the time-dependent mechanical formulation, using the Heaviside step function for completely cutted elements and the cohesive model for crack tips. In order to find the propagation parameters, a crack evolution model is proposed. The numerical implementation is achieved in new explicit FE module. A numerical example is proposed for proving the computational efficiency of this new module.

A Dynamic Crack Propagation Criteria for XFEM, Based on Path-Independent Integral Evaluation

The eXtended Finite Element Method (XFEM) has been successfully used for several years for the numerical analysis of cracked structures under statically and later under dynamically loadings. Based on Partition of Unity Method, the XFEM was developed at Northwestern University (Moes et al. [1]) firstly as a method for analysing crack growth without remeshing, using special enrichment functions to model discontinuous displacement fields. Since, the method was continuously improved and applied to various domains of fracture mechanics. The dynamic crack propagation is one of them and an important contribution for its modelling by XFEM was given by Belytschko et al. [2].

A methodology for large scale finite element models, including multi-physic, multi-domain and multi-timestep aspects

This works concerns the development of a virtual prototyping tool dedicated to electro-thermo-mechanical simulation of power converters. The FEM code, written using an object-oriented language, includes a dual Schur Domain Decomposition Method. The solving of problems including floating subdomains can be performed in steady-state cases, whereas one can couple multi-timestep implicit and explicit integration schemes in transient analysis. The last part of this work is about the study of an industrial benchmark concerning the power converters used in railway transport: the electro-thermal simulation of a switch in transient analysis. This example allows to compare different strategies of tearing into subdomains and the use of different timesteps on the same structure.