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

Abstract

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.

XFEM Modeling of Interface Failure in Adhesively Bonded Fiber‐Reinforced Polymers

“…It has since then been successfully applied to the modeling of material interfaces. [11][12][13] A comprehensive review of the method is presented by Fries and Belytschko. [14] …”

“…A macroscopic strain state e m that results in a uni-axial stress is applied to the RVE. [12] The overall deformation in the loading direction is prescribed in terms of the macrostrain e m while the boundary perpendicular to the loading direction is assumed to be traction free. This allows for an arbitrary lateral contraction.…”

“…The properties of the roving are extracted from a linear elastic homogenization in ref. [12] An elastic modulus E R ¼ 17831 MPa (transversal) and a Poisson ratio n R ¼ 0:39 have been used in the 2D model. The actually viscoelastic behavior of the polypropylene matrix and the adhesive is approximated by the instantaneous moduli E M ¼ 1900 MPa [23] and E A ¼ 1620 MPa, [31] respectively.…”

A Large Strains Finite Element Multiscale Approach

“…However, only a few are dealing with large strains. Thus, there are multiscale approaches dealing with small strains [1,2,3,4,5,6], ductile damage [7], plasticity [8,9,10], quasi-brittle materials [11,12,13,14], laminates [15], filament-wound composites [16], shape memory alloy composites [17],randomly distributed heterogeneities [18], fracture [19,20,21,22,23,24], fracturing reinforced composites based in an embedded cell methodology [25], for the solution of granular materials problems with periodically repeated aggregate configurations [26]. A computational multiscale technique using shells for system of heterogeneous thin sheets with in-plane quadrature points at the macroscale was proposed by [27].…”

XFEM modeling of inelastic material behavior of composite

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In the present contribution the authors applied numerical homogenization techniques to predict the effective material behavior of composite based on the simulation of a representative volume element (RVE) [1]. An enriched displacement approximation (XFEM) is used to describe weak and strong discontinuities within the displacement field, independent from the underlying FE mesh.

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