The effectiveness of studying inter-laminar delamination in laminated composites with the help of thickness-stretch shell elements which utilize a 3-D material model sub-routine as compared to the traditional plane-stress shell elements has been investigated using a non-linear finite element solver (LS-DYNA®). A strain-rate-dependent micro-mechanical material model using ply-level progressive failure criteria has been used to simulate the initiation and propagation of delamination. A methodology of assigning physical significance to the choice of damage parameters has been presented. The numerical delamination growth has been qualitatively analyzed against the experimental C-scan images for multiple impact events on different composite plates.
CamanhoPPHallettSR. Numerical modelling of failure in advanced composite materials, Cambridge, UK: Woodhead Publishing, 2015.
4.
Pagano NJ and Schoeppner GA. Delamination of polymer matrix composites: problems and assessment. In: Kelly A and Zweben C (eds) Comprehensive composite materials. Vol 2. Amsterdam, Netherlands: Elsevier, 2003, pp.433–528.
5.
TalrejaRVarnaJ. Modeling damage, fatigue and failure of composite materials, Cambridge, UK: Woodhead Publishing, 2016.
6.
ChristensenRM. Mechanics of composite materials, Hoboken, NJ: John Wiley & Sons, Inc., 1979.
7.
BelytschkoTLinJIChen-ShyhT. Explicit algorithms for the nonlinear dynamics of shells. Comput Methods Appl Mech Eng1984; 42: 225–251.
8.
SimoJCRifaiMSFoxDD. On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching. Comput Meth Appl Mech Eng1990; 81: 91–126.
9.
ParischH. A continuum-based shell theory for non-linear applications. Int J Numer Methods Eng1995; 38: 1855–1883.
10.
HauptmannRSchweizerhofK. A systematic development of ‘solid-shell’ element formulations for linear and non-linear analyses employing only displacement degrees of freedom. Int J Numer Meth Eng1998; 42: 49–69.
11.
DollSSchweizerhofKHauptmannR, et al.On volumetric locking of low-order solid and solid‐shell elements for finite elastoviscoplastic deformations and selective reduced integration. Eng Comput2000; 17: 874–902.
12.
BüchterNRammE. Shell theory versus degeneration—a comparison in large rotation finite element analysis. Int J Numer Methods Eng1992; 34: 39–59.
13.
BüchterNRammERoehlD. Three-dimensional extension of non-linear shell formulation based on the enhanced assumed strain concept. Int J Numer Methods Eng1994; 37: 2551–2568.
14.
El-AbbasiNMeguidSA. New shell element accounting for through-thickness deformation. Comput Methods Appl Mech Eng2000; 189: 841–862.
15.
BetschPGruttmannFSteinE. A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains. Comput Methods Appl Mech Eng1996; 130: 57–79.
16.
BischoffMRammE. Shear deformable shell elements for large strains and rotations. Int J Numer Meth Eng1997; 40: 4427–4449.
17.
CardosoRPRYoonJW. One point quadrature shell element with through-thickness stretch. AIP Conf Proc2005; 778 A: 739–744.
18.
BraunMBischoffMRammE. Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates. Comput Mech1994; 15: 1–18.
TabieiAAminjikaraiSB. A strain-rate dependent micro-mechanical model with progressive post-failure behavior for predicting impact response of unidirectional composite laminates. Compos Struct2009; 88: 65–82.
21.
TabieiAYiWGoldbergR. Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation. Int J Non Linear Mech2005; 40: 957–970.
22.
TabieiAChenQ. Micromechanics based composite material model for crashworthiness explicit finite element simulation. J Thermoplast Compos Mater2001; 14: 264–289.
23.
MedikondaSTabieiAHammR. A comparative study on the effect of representative volume cell (RVC) boundary conditions on the elastic properties of a micromechanics based unidirectional composite material model. Int J Compos Mater2017; 7: 51–71.
24.
GoldbergRKRobertsGDGilatA. Implementation of an associative flow rule including hydrostatic stress effects into the high strain rate deformation analysis of polymer matrix composites. J Aerosp Eng2005; 18: 18–27.
25.
ZhengXBiniendaWK. Rate-dependent shell element composite material model implementation in LS-DYNA. J Aerosp Eng2008; 21: 140–151.
WangZXiaY. Experimental evaluation of the strength distribution of fibers under high strain rates by bimodal Weibull distribution. Compos Sci Technol1998; 57: 1599–1607.
28.
WangZXiaYYangB. A statistical model and experimental study of the strain rate and temperature dependence of the strength of fibers. Appl Compos Mater1996; 3: 89–101.
29.
Qu J and Cherkaoui M. Effective properties of fiber-reinforced composite laminates. In: Fundamentals of Micromechanics of Solids. Hoboken, NJ: John Wiley & Sons, Inc., pp. 214–244.
30.
YenC-FGroundAP. A ballistic material model for continuous – fiber reinforced composites. Int J Impact Eng2012; 46: 11–22.
31.
MurrayYSchwerL. Implementation and verification of the fiber composite damage models. Fail Criteria Anal Dyn Response ASME AMD1990; 107: 21–30.
MatzenmillerALublinerJTaylorRL. A constitutive model for anisotropic damage in fiber-composites. Mech Mater1995; 20: 125–152.
34.
WilliamsKVVaziriR. Application of a damage mechanics model for predicting the impact response of composite materials. Comput Struct2001; 79: 997–1011.
35.
WilliamsKVVaziriRPoursartipA. A physically based continuum damage mechanics model for thin laminated composite structures. Int J Solids Struct2003; 40: 2267–2300.
36.
Yen C-F. Ballistic impact modelling of composite materials. In: Proceedings of the 7th International LS-DYNA Users Conference, Dearborn, Michigan, 2002, pp.15–26.
37.
BazantZOhB. Crack band theory of concrete. Mater Struct1983; 16: 155–177.
38.
PinhoSTIannucciLRobinsonP. Physically based failure models and criteria for laminated fibre-reinforced composites with emphasis on fibre kinking. Part II: FE implementation. Compos A Appl Sci Manuf2006; 37: 766–777.
39.
CousignéOMoncayoDCoutellierD, et al.Development of a new nonlinear numerical material model for woven composite materials accounting for permanent deformation and damage. Compos Struct2013; 106: 601–614.
40.
AminjikaraiSBTabieiA. A strain-rate dependent 3-D micromechanical model for finite element simulations of plain weave composite structures. Compos Struct2007; 81: 407–418.
41.
Stander N, Roux W, Basudhar A, et al. LS-OPT® User’s Manual – a design optimization and probabilistic analysis tool for the engineering analyst, Livermore Software Technology Corporation, December 2015.
42.
HaSKSpringerGS. Nonlinear mechanical properties of a thermoset matrix composite at elevated temperatures. J Compos Mater1989; 23: 1130–1158.
43.
Delfosse D, Poursartip A, Coxon BR, et al. Non-penetrating impact behavior of CFRP at low and intermediate velocities. In: Proceedings of symposium on composite materials: fatigue and fracture: fifth volume (ed. R Martin), 4 May 1993 to 6 May 1995, pp.333–350, West Conshohocken, PA: ASTM International, 1995.
44.
DaviesGAOZhangX. Impact damage prediction in carbon composite structures. Int J Impact Eng1995; 16: 149–170.
45.
ChoiHYChangF-K. A model for predicting damage in graphite/epoxy laminated composites resulting from low-velocity point impact. J Compos Mater1992; 26: 2134–2169.
