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An approach to incorporate the coupling between the shear compliance and in-plane tension of woven engineering fabrics, in finite-element-based numerical simulations, is described. The method involves the use of multiple input curves that are selectively fed into a hypoelastic constitutive model that has been developed previously for engineering fabrics. The selection process is controlled by the current value of the in-plane strain along the two fibre directions using a simple algorithm. Model parameters are determined from actual experimental data, measured using the Biaxial Bias Extension test. An iterative process involving finite element simulations of the experimental test is used to normalise the test data for use in the code. Finally, the effectiveness of the method is evaluated and shown to provide qualitatively good predictions.

Press forming of woven engineering fabrics can be used to create complex geometries, suitable for subsequent liquid moulding and cure for the manufacture of composite parts [

The commercial FE code Abaqus Explicit has been used throughout this investigation. The FE model uses the same combination of mutually constrained truss elements (representing the high tensile stiffness fibres) and membrane elements (representing the shear properties of the fabric) as that described in [

FE unit cell representation of textile structure modelled using mutually constrained membrane and truss elements (from Harrison et al. [

The mesh is automatically generated using an in-house mesh generation code. A simple approximate homogenisation method has been used to calculate truss dimensions and mechanical properties. Using the equation
^{2} per metre in Harrison et al. [

The truss properties chosen for the truss elements here (stiffness = 6 GPa, length = 0.01237 m, circular cross-sectional area 1 × 10^{−6} m^{2} gives an area per unit length, ^{2} per m) produce a sheet with a tensile response between about 5 and 13 times lower than an actual woven glass fabric, and for simplicity, the nonlinear tensile behaviour in the tows due to fabric crimp, for example, [

The membrane elements provide no contribution to the tensile stiffness of the mesh and are only used to add shear resistance to the sheet. The membrane elements have an initial thickness of 0.0002 m with a Poisons ratio of 0. The shear stresses within the membrane elements are modelled using an enhanced version of the shear part of the original non-orthogonal constitutive model [

Implementation of the shear-tension coupled S-NOCM involves linking the shear parameters in the original S-NOCM model with the tensile stresses (or equivalently the tensile strains) acting along the warp and weft fibre directions in the fabric. Like the shear angle, the tensile strains are accessible as state-dependent variables within the Abaqus user-subroutine. In this section, a method of producing the same shear-tension coupling in the numerical model as that measured in actual woven engineering fabrics is described. The technique involves a four-stage process, as follows.

This involves simulating the BBE test; details of the actual experiments can be found in [

The BBE FE model. Force boundary conditions are applied to the right and left centrally located node sets, and vertical displacement boundary conditions are applied to the upper and lower centrally located node sets. The colour legend indicates the shear angle. The three different deformations occurring in Regions A, B and, C of the test specimen are clearly visible. The shear angle in Region A is taken from the highlighted element.

Note that to determine

This involves determining the average tensile strains,

This involves implementing the shear-tension coupling in the VUMAT user-subroutine. To do this, code has been added within the original VUMAT user-subroutine for the S-NOCM to compare the value of

The flow chart of shear-tension coupling algorithm which runs for each membrane element at every time increment during a simulation.

Thus, the shear force input curve is now a function of both the shear angle and the fibre strain within the membrane element. The process is illustrated in Figure

Shear force plotted against the shear angle,

Consider an element that has a shear angle of 45° at time,

At this point, it is possible to compare the results of the enhanced S-NOCM against the experimental input data, as shown in Figure

Comparison between the experimental [

This involves a simple normalisation procedure aimed at normalising the experimental input curves (which have to be supplied as shear force per unit length of fabric). By correctly normalising the experimental biaxial bias-extension curves, the numerical simulations should produce approximately the same shear force versus shear angle predictions as those observed in experiments. To do this, an approximate procedure is used here by the following simple iterative method. (i) The input shear force versus shear angle curves are divided by the predicted shear force versus shear angle curves to produce a ratio (also a function of the shear angle). (ii) Polynomial functions,

Comparison between the experimental and the predicted results using the coupled S-NOCM and normalized

To test the effectiveness of the modelling approach, two final BBE simulations are conducted, this time using transverse loads increasing linearly in time from 5 N to 100 N rather than using constant transverse loads. In Figures

Evaluation of the coupled S-NOCM (a) and (b). The faint grey lines are the experimental results from [

As expected, the axial force predictions of the enhanced shear-tension coupled S-NOCM, made using increasing transverse loads, move across the normalised numerical predictions generated using constant transverse loads (the black curves). The different transverse loads versus shear angle profiles,

The first is the choice of elements used to create the average strain curves,

The second is the normalisation technique used in this work. The very simple normalisation procedure used here takes no account of the shear-tension coupling in the fabric, and a more rigorous method was recently proposed in [

The third is the method of calculating the stress increment at each time step. A tangent stiffness matrix has been used to determine this stress increment; that is,

Despite the irregularities in the predictions of the shear-tension coupled model under certain in-plane loading conditions, it is clear that the technique proposed here produces a shear-tension coupling similar to that seen in actual experiments. Future work will focus on improving the accuracy of the method, though the model predictions are considered to be sufficiently accurate at this stage to begin to examine the question of whether or not and also under which conditions, the influence of a shear-tension coupling on the shear angle and wrinkling predictions of complex forming simulations, is important.

A method of modelling the coupling between shear compliance and in-plane tension in woven engineering fabrics has been demonstrated. The method is similar to that used previously to create rate-dependent “viscous” behaviour using a hypoelastic model [

Please note that none of the authors of the paper has a direct financial relation with the commercial identity mentioned in this paper that might lead to a conflict of interests for any of them.

The authors wish to express their thanks for The Public Treasury of Libyan Society, the Royal Academy of Engineering for a Global Research Award (10177/181), and the National Research Foundation (NRF) for sponsoring this research through the SRC/ERC Program of MOST/KOSFE (R11-2005-065).