Multiscale XFEM-modelling and simulation of the inelastic material behaviour of textile-reinforced polymers



This paper addresses the multiscale simulation of fibre-reinforced polymers. The considered composite materials exhibit a hierarchical material structure with three distinct length scales—micro, meso and macro. This feature of the morphology allows for the application of homogenization techniques based on a representative volume element (RVE) that is entirely typical for the local, periodic material structure. The effective macroscopic material behaviour of the composite can be predicted from the properties of the individual constituents and the geometric arrangement of the reinforcing fibres based on the simulation of the material behaviour in the RVE.

The heterogeneous material structure in an RVE is modelled by the eXtended finite element method (XFEM). To this, two special element types, called X-element and 2X-element, are derived. They can represent one or two material interfaces within the element domain. For an efficient modelling process, an automated model generation procedure that determines the required element types, locates the material interfaces and performs the subdivision of the X-elements into tetrahedral integration domains has been developed. Problems related to a consistent interface approximation and a continuous displacement field are discussed.

In the generated RVE models, a viscoplastic material model accounts for the inelastic material behaviour of the polymeric matrix, whereas the glass-fibres are assumed to have a linear elastic stress–strain behaviour. Using periodic displacement boundary conditions, effective stress–strain curves are computed for glass-fibre-reinforced polypropylene with unidirectional and woven arrangements of the reinforcing fibres. Copyright © 2010 John Wiley & Sons, Ltd.