SUMMARYThis 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.
SUMMARYThe FE-simulation of inhomogeneous structures, such as composite materials, biological tissues or foams, requires the generation of respective finite element meshes. With increasing complexity of the inner architecture of such structures, this becomes a time-consuming and laborious task. Additionally, the risk of forming bad-shaped elements that may lead to ill-conditioned numerical problems grows significantly. A solution to this problem provides the extended finite element method (XFEM). Thereby, the interface between different materials is represented by a local enrichment of the displacement approximation. As a consequence of this, the element boundary need not be aligned to the interface.In order to improve the accuracy of the interface approximation, the development of a plane element based on the XFEM and quadratic shape functions will be presented. This element allows for the description of curved material interfaces. The computation of the element stiffness matrix requires a numerical integration process that accounts for discontinuous fields. Regarding a linear element formulation, this can be achieved by an adapted triangulation of the element domain. However, in the case of a curved interface this solution is not applicable. Hence, non-uniform rational B-Spline (NURBS) surfaces are used to evaluate the integrals numerically.Finally, the results of different examples will show the general properties such as the accuracy of the numerical integration procedure and the convergence behavior of this element formulation.
Novel textile reinforced composites provide an extremely high adaptability and allow for the development of materials whose features can be adjusted precisely to certain applications. A successful structural and material design process requires an integrated simulation of the material behaviour, the estimation of the effective properties which need to be assigned to the macroscopic model and the resulting features of the component. In this context two efficient modelling strategies -the Binary Model [1] and the Extended Finite Element Method (X-FEM) [2] -are used to model materials which exhibit a complex structure on the meso-scale. For these investigations the focus is set on composites made of glass fibers, thermoset or thermoplastic matrices and on the application of commingled thermoplastic and glass fibers. Homogenization techniques are applied to compute effective macroscopic stiffness parameters. Problems arising from a complex textile reinforcement architecture, e.g. bi-or multiaxial weft-knit, woven and braided fabrics, in combination with a high fiber volume fraction will be addressed and appropriate solutions are proposed. The obtained results are verified by experimental test data. The macroscopic stress and strain fields in a component are used for optimisation of the construction and the material layout. These distributions are computed in a global structural finite element analysis. Based on the global fiber orientation the required macroscopic material properties obtained from homogenization on the meso-scale are mapped to the model of the structural part. The configuration of the fiber-orientation and textile shear deformation in complex structural components caused by the manufacturing process is determined by a three-dimensional optical measurement system.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.