Recently, as a part of the third World-Wide Failure Exercise (WWFE-III), the author provided a modelling capability, entitled ‘Energy methods for modelling damage in laminates’, published in this special issue (2013, Vol 20–21, pages 2613–2640). This paper describes full details and the mathematical basis of the author’s methods used to predict the properties of undamaged laminates and the development of damage in laminates, based on an energy balance methodology.
McCartneyLN. Predicting transverse crack formation in cross-ply laminates resulting from microcracking. Comput Sci Technol1998; 58: 1069–1081.
2.
SodenPDHintonMJKaddourAS. Lamina properties, lay-up configurations and loading conditions for a range of fibre reinforced composite laminates. Comput Sci Technol1998; 58: 1001–1254. and other papers in the same special issue. Part B of the exercise is published in Comput Sci Technol 2002; 62: 1481–1797. Part B of the exercise is published in Comput Sci Technol 2004; 64: 321–604.
3.
McCartneyLN. Model to predict effects of triaxial loading on ply cracking in general symmetric laminates. Comput Sci Technol2000; 60: 2255–2279. See errata in Comput Sci Technol 2002; 62: 1273–1274.
4.
McCartneyLN. Predicting ply crack formation and failure in laminates, Part B in International Failure Exercise. Comput Sci Technol2002; 62: 1619–1631.
5.
McCartney LN and Pierse C. Stress transfer mechanics for multiple-ply laminates subject to bending. NPL Report CMMT(A)55, February 1997.
6.
McCartney LN and Pierse C. Stress transfer mechanics for multiple ply laminates for axial loading and bending. In: Proceedings 11th international conference on composite materials, Gold Coast, Australia, 14–18 July, 1997, vol. V, pp.662–671. Australian Composites Structural Society/Woodhead Publishing Ltd.
7.
McCartney LN. Predicting ply crack formation in cross-ply laminates subject to generalised plane strain bending. In: Procedings 6th international conference on deformation and fracture of composites, Manchester, 4–5 April 2001, pp.57–66. London: IOM Communications Limited, the Institute of Materials.
8.
McCartney LN and Byrne MJW. Energy balance method for predicting cracking in cross-ply laminates during bend deformation. In: Proceedings 10th international conference on fracture (ICF-10), advances in fracture research, Honolulu, 2–6 December 2001.
9.
McCartney LN. Approximate method of predicting ply crack formation in general symmetric laminates subject to biaxial loading and bending. In: Electronic proceedings of 13th European conference on composite materials (ECCM-13), Stockholm, June 2008.
10.
McCartneyLN. Energy-based prediction of progressive ply cracking and strength of general symmetric laminates using an homogenization method. Compos A2005; 36: 119–128.
11.
McCartneyLN. Energy-based prediction of failure in general symmetric laminates. Eng Fract Mech2005; 72: 909–930.
12.
Love AEH. A treatise on the mathematical theory of elasticity. Chapter XI, 4th ed., 1944.
Eringen AC. Mechanics of continua. New York: John Wiley & Sons, 1967.
15.
McCartneyLNSchoeppnerGA. Predicting the effect of non-uniform ply cracking on the thermoelastic properties of cross-ply laminates. Comput Sci Technol2002; 62: 1841–1856.
16.
BoxGEPMullerME. A note on the generation of random normal deviates. Ann Math Statist1958; 29: 610–611.
17.
McCartneyLN. Energy methods for modelling damage in laminates (WWFE-III). J Compos Mater2013; 2013; 47(20–21): 2613–2640.
18.
Hannaby SA. The solution of ordinary differential equations arising from stress transfer mechanics of general symmetric laminates. NPL Report CISE 13/97, April 1997.
19.
Hannaby SA. The solution of ordinary differential equations arising from stress transfer mechanics. NPL Report DITC 223/93, November 1993.
20.
Smith BT, Boyle JM, Dongarra JJ, et al. Matrix eigensystems routines – EISPACK guide. Lecture Notes in Computer Science, vol. 6, 2nd ed. New York, Heidelberg, Berlin: Springer-Verlag, 1976.
21.
DongarraJJBunchJRMolerCB. LINPACK user guide, Philadelphia: SIAM, 1979.
