ELEMENT-LOCAL STRESS RECOVERY IN LINEAR SHELLS

Other conference contribution, 2019

The introduction of laminated fibre reinforced polymers (FRP) in the automotive industry is strongly dependent on accurate and efficient modelling tools to predict the correct energy absorption in crash simulations. To increase the efficiency of such large-scale simulations, we have implemented an adaptive enrichment methodology for modelling of multiple and arbitrarily located delamination cracks using an equivalent single-layer shell model [1] as a user element in the commercial FE solver LS-DYNA. In summary the methodology starts the simulation with one shell element through the thickness. By identifying critical ply interfaces using a recovery technique of the transverse stresses, the element can then firstly be through-the-thickness refined to improve the stress prediction and secondly cohesive interface elements can be inserted such that delaminations can be modelled.

However, in [1] the stress recovery technique was based on a non-local super-convergent patch polynomial fit, which is not suitable for a user LS-DYNA implementation as non-local information is hard to obtain. Instead we aim to utilize the Extended 2D recovery technique by Rolfes and colleagues [2], [3]. A known drawback with this technique is that the recovery of the transverse normal stress, which is made from the in-plane derivatives of the shear force, requires quadratic approximation of the out-of-plane displacements. Again, this is not suitable for our user element implementation in LS-DYNA, which we choose to base on a solid shell formulation with linear approximation due to numerical efficiency.

Several authors have presented alternatives to estimate the transverse normal stress in linear shell elements, e.g. by neglecting shear forces [4] or making an assumption on the ratio of the shear force variation [5]. In this contribution we will examine the possibility to utilise the transverse normal stress from the FE-solution, available when using solid shell elements. We will benchmark this approach in a range of geometries with different modelling resolutions. If successful, our methodology will feature an element-wise stress recovery technique capable of estimating all transverse stresses even using a linear element. In the long run the methodology can enable computationally efficient simulations of delamination failure in composite structures and help to develop crash structures made of laminated FRP.   

References

[1]      J. Främby, M. Fagerström, and J. Brouzoulis, Int. J. Numer. Methods Eng., vol. 112, no. 8, pp. 882–908, Nov. 2017.

[2]      R. Rolfes and K. Rohwer, Int. J. Numer. Methods Eng., vol. 40, pp. 51–60, 1997.

[3]      R. Rolfes, K. Rohwer, and M. Ballerstaedt, Comput. Struct., vol. 68, no. 6, pp. 643–652, Sep. 1998.

[4]      R. Roos, G. Kress, and P. Ermanni, Compos. Struct., vol. 81, no. 3, pp. 463–470, 2007.

[5]      R. Tanov and A. Tabiei, Compos. Struct., vol. 76, no. 4, pp. 338–344, 2006.