Woven fabrics UMAT- a coupled material model
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Abstract
One of the advantages of woven fabrics over unidirectional prepregs is their superior formability thanks to the large shear deformation capability. There exists, however, a limit on the shear deformation of woven fabrics, namely the wrinkling. Applying tension to delay wrinkling during forming processes, a consequence of the inherent coupling in woven fabrics, is widely known to the industry. Yet, inherent coupling – change in the effective material properties of a given direction of the fabric due to the applied deformation in other directions - has not been fully understood and implemented in the forming simulations of fabric reinforcements. Coupling should be incorporated in numerical optimization routines to accurately predict the deformation of the material under complex forming set-ups, and more importantly to predict a realistic yarn tension level that can suppress wrinkles. Towards this goal, a new coupled non-orthogonal model which predicts not only the stress-strain path, but also the critical point (shear wrinkling) of the woven fabrics should be proposed and implemented in a numerical simulation. The theory of the material model is thoroughly discussed in the submitted article. In summary, a coupled non-orthogonal hypoelastic constitutive model along with a criterion for wrinkling in terms of coupling are offered. To show its application, the model is implemented in ABAQUS via a UMAT code to predict the stress and strain fields as well as the onset of wrinkling under large shear deformations.
The popular user subroutine to study the solid mechanics of woven fabrics is VFabric subroutine, which is deeply explained in ABAQUS (DS Simulia) user manual. In spite of taking non-orthogonality into account, the inherent coupling is ignored in the VFabric subroutine. The code provided here is able to take the inherent coupling into consideration, resulting in more accurate prediction of the response of woven fabrics under forming processes. Moreover, the VFabric subroutine is efficient for dynamic explicit analyses and cannot be used for dynamic implicit and static FE simulations. Although the explicit analysis is more practical for studying forming process; its precision, in particular for wrinkling prediction, is much weaker than implicit analysis. Also, coupled thermal-mechanical analysis to consider the effect of temperature on the mechanical properties of woven fabrics can be performed using the implicit approach. Hence, the presented subroutine has been written for the implicit solutions in ABAQUS. When ABAQUS calls the UMAT_Woven Fabrics, the subroutine is provided with the inputs such as current stress as well as strain components and solution dependent state variables (SDV). The Subroutine undertakes the stress analysis and predicts the response of woven fabrics in the current time increment by providing outputs at the end of the increment. These outputs (stress, strain and SDV) will be used as next increment inputs.
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