The stacked thick-shell modelling approach is investigated in the frame of explicit dynamics FE method for the simulation of composite structures. The methodology is developed for static and dynamic loading conditions and demonstrated in the case of three-point bending of laminated strips. For the validation of the stacked thick-shell modelling approach, experimental testing using laminated short beam shear coupons of the AS4/8552 composite material system is performed and the interlaminar shear strength under impact loading is determined. The specimen dynamic tests were performed using a drop tower apparatus and a specially designed three-point loading fixture. In parallel, conventional three-dimensional solid models are also analysed for comparison purposes. Test results correlate well to the respective numerical predictions, demonstrating the accuracy of the stacked thick-shell approach and the efficiency it provides in interlaminar stresses prediction, which makes the proposed approach suitable for large-scale composite structures simulation, with emphasis in delamination damage propagation.
AbrateS.: ‘Impact on composite structures’, 1998, Cambridge, Cambridge University Press.
2.
AgrawalS., SinghK. K. and SarkarP. K.: ‘Impact damage on fibre-reinforced polymer matrix composite – a review’, J. Compos. Mater., 2014, 48, 317–332. doi: 10.1177/0021998312472217
3.
‘Standard test method for short-beam strength of polymer matrix composite materials and their laminates’, D2344, ASTM, 2000.
4.
‘Standard test method for flexural properties of unreinforced and reinforced plastics and electrical insulating materials by four-point bending’, D6272, ASTM, 2002.
5.
‘Standard test method for shear properties of composite materials by the V-Notched beam method’, D5379, ASTM, 1999.
6.
‘Standard test method for in-plane shear strength of reinforced plastics’, D3846, ASTM, 2002.
7.
ReissnerE.: ‘The effect of transverse shear deformation on the bending of elastic plates’, J. Appl. Mech., 1945, 12, 69–77.
8.
MindlinR. D.: ‘Influence of rotator inertia and shear on flexural motions of isotropic, elastic plates’, J. Appl. Mech., 1951, 18, 31–38.
9.
WhitneyJ. M. and PaganoN. J.: ‘Shear deformation in heterogeneous anisotropic plates’, J. Appl. Mech., 1945, 37, (4), 1031–1036. doi: 10.1115/1.3408654
10.
ReddyJ. N.: ‘Mechanics of laminated composite plates and shells’, 2004, Boca Raton, CRC Press.
11.
JohnsonA. F., PickettA. K. and RozyckiP.: ‘Computational methods for predicting impact damage in composite structures’, Compos. Sci. Technol., 2001, 61, (15), 2183–2192. doi: 10.1016/S0266-3538(01)00111-7
12.
LampeasG. and FotopoulosK.: ‘Interlaminar stresses calculation using a stacked-shell finite element modeling approach’, Int. J. Appl. Mech., 2015, 7, 5. doi: 10.1142/S1758825115500672
13.
HughesT. J. R. and LiuW. K.: ‘Nonlinear finite element analysis of shells: Part I. three-dimensional shells’, Comput. Methods Appl. Mech. Eng., 1981, 26, 331–362. doi: 10.1016/0045-7825(81)90121-3
14.
HughesT. J. R. and LiuW. K.: ‘Nonlinear finite element analysis of shells-part II. Two-dimensional shells’, Comput. Methods Appl. Mech. Eng., 1981, 27, 167–181. doi: 10.1016/0045-7825(81)90148-1
15.
BelytschkoT., LinJ. I. and TsayC. S.: ‘Explicit algorithms for the nonlinear dynamics of shells’, Comp. Methods Appl. Mech. Eng., 1984, 42, 225–251. doi: 10.1016/0045-7825(84)90026-4
16.
LiuW. K., BelytschkoT., OngJ. S. J. and LawE.: ‘Use of stabilization matrices in non-linear analysis’, Eng. Comput., 1985, 2, 47–55. doi: 10.1108/eb023600
17.
LiuW. K., HuY. K. and BelytschkoT.: ‘Multiple quadrature underintegrated finite elements’, Int. J. Num. Meths. Engrg., 1994, 37, 3263–3289. doi: 10.1002/nme.1620371905
18.
LiuW. K., GuoY., TangS. and BelytschkoT.: ‘A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis’, Comput. Methods Appl. Mech. Eng., 1998, 154, 69–132. doi: 10.1016/S0045-7825(97)00106-0
19.
HallquistJ. O.: ‘LS-DYNA theory manual’; 2015, Livemore, CA, Livermore Software Technology Corporation.
20.
ChangF. K. and ChangK. Y.: ‘A progressive damage model for laminated composites containing stress concentrations’, J. Compos. Mater., 1987, 21, (9), 834–855. doi: 10.1177/002199838702100904
TuronA., DavilaC. G. and CamanhoP. P.: ‘An engineering solution for using coarse meshes in the simulation of delamination with cohesive zone modeling’, NASA Technical Report NASA/TM-2005-213547, Langley Research Center, Hampton, VA, 2005.
23.
WoelkeP., ChanK. K., DaddazioR., AbboudN. and VoyiadjisG. Z.: ‘Analysis of shear flexible layered isotropic and composite shells by “EPSA”’, Shock Vib., 2012, 19, 459–475. doi: 10.1155/2012/179879
DonaldsonB. K.: ‘Analysis of aircraft structures’, 2008, New York, Cambridge University Press.
26.
ChristiansenA. W., LilleyJ. and ShortallJ. B.: ‘A three point bend test for fibre-reinforced composites’, Fibre Sci. Technol., 1974, 7, 1–13. doi: 10.1016/0015-0568(74)90002-5
27.
XieM. and AdamsD. F.: ‘Study of three- and four-point shear testing of unidirectional composite materials’, Composites, 1995, 26, 653–659. doi: 10.1016/0010-4361(95)98914-7
28.
WangZ. and ChengL.: ‘Effect of material parameters on stress wave propagation during fast upsetting’, Trans. Nonferrous Met. Soc. China, 2008, 18, 1189–1195. doi: 10.1016/S1003-6326(08)60203-4
29.
WiegandJ.: ‘Constitutive modelling of composite materials under impact loading’, PhD Thesis, University of Oxford, UK, 2008.
30.
DanielsB. K., HarakasN. K. and JacksonR. C.: ‘Short beam shear tests of graphite fiber composites’, Fibre Sci. Technol., 1971, 3, 187–208. doi: 10.1016/0015-0568(71)90002-9
31.
MottP. H., SmallhornJ. M., CampbellK. W., SchraderH. L., CartwrightC. L. and FinckD. G.: ‘Comparison of buckling of an arched, rubber-core sandwich composite panel to finite element modeling’, Compos. A: Appl. Sci. Manuf., 2011, 42, 843–848. doi: 10.1016/j.compositesa.2011.03.013
32.
CavallaroP. V.: ‘Effects of weave styles and crimp gradients in woven Kevlar/epoxy composites’, Exp. Mech., 2015. doi:10.1007/s11340-015-0075-4
