This paper presents the results from the authors’ participation in the Air Force Research Laboratory’s Damage Tolerance Design Principles Program. The Eigendeformation-based reduced order homogenization method was employed to predict the mechanical response of a suite of open hole and unnotched IM7/977-3 composite laminates under static tension and compression. Damage accumulation, effective stiffness, and ultimate strength blind predictions are included in addition to the results of the recalibration study. In blind predictions, the proposed multiscale model produced predictions with an average error of 13.1% compared to the experiments for static ultimate strength and 13.6% for stiffness. After recalibration, the average prediction error was improved to 8.7% for static ultimate strength and 4.4% for stiffness. Details of the blind predictions and the recalibration are discussed.
HouTYWuX-H. A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys1997; 134: 169–189.
2.
WeinanEEngquistB. The heterogenous multiscale methods. Commun Math Sci2003; 1: 87–132.
3.
GhoshSLeeKRaghavanP. A multi-level computational model for multi-scale damage analysis in composite and porous materials. Int J Solids Struct2001; 38: 2335–2385.
4.
OskayC. Variational multiscale enrichment for modeling coupled mechano-diffusion problems. Int J Numer Methods Eng2012; 89: 686–705.
5.
OskayC. Variational multiscale enrichment method with mixed boundary conditions for modeling diffusion and deformation problems. Comput Methods Appl Mech Eng2013; 264: 178–190.
6.
BabuskaIHomogenization and application. Mathematical and computational problems. In: HubbardB (ed). Numerical solution of partial differential equations - III, SYNSPADE, New York: Academic Press, 1975, pp. 89–115.
7.
BenssousanALionsJLPapanicolaouG. Asymptotic analysis for periodic structures, Amsterdam: North-Holland, 1978.
8.
SuquetPMElements of homogenization for inelastic solid mechanics. In: Sanchez-PalenciaEZaouiA (eds). Homogenization techniques for composite media, Berlin: Springer-Verlag, 1987, pp. 193–198.
9.
Sanchez-PalenciaE. Non-homogeneous media and vibration theory. Volume 127 of Lecture notes in physics, Berlin: Springer-Verlag, 1980.
10.
TeradaKKikuchiNNonlinear homogenization method for practical applications. In: GhoshSOstoja-StarzewskiM (eds). Computational methods in micromechanics, vol AMD-212/MD-62, New York: ASME, 1995, pp. 1–16.
11.
FishJShekKPandheeradiM. Computational plasticity for composite structures based on mathematical homogenization: theory and practice. Comput Methods Appl Mech Eng1997; 148: 53–73.
12.
MieheCSchröderJSchotteJ. Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput Methods Appl Mech Eng1999; 171: 387–418.
13.
Kouznetsova VG. Computational homogenization for the multi-scale analysis of multi-phase materials. PhD Thesis, Eindhoven University of Technology, 2002.
14.
OskayCFishJ. Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput Methods Appl Mech Eng2007; 196: 1216–1243.
15.
CrouchROskayC. Symmetric mesomechanical model for failure analysis of heterogeneous materials. Int J Multiscale Comput Eng2010; 8: 447–461.
16.
DvorakGJBenvenisteY. On transformation strains and uniform fields in multiphase elastic media. Proc Roy Soc London1992; A437: 291–310.
17.
DvorakGJWafaAMBahei-El-DinYA. Implementation of the transformation field analysis for inelastic composite materials. Comput Mech1994; 14: 201–228.
18.
CrouchROskayC. Experimental and computational investigation of progressive damage accumulation in CFRP composites. Composites Part B2013; 48: 59–67.
19.
Bogdanor MJ and Oskay C. Application of reduced order multiscale homogenization to assess and quantify the benefits of applying damage tolerant design principles to advanced composite aircraft structures. In: Proceedings of the 56th AIAA Structures, Structural Dynamics, and Materials, Kissimmee, Florida, 5–9 January 2015.
20.
HuiTOskayC. Computational modeling of polyurea-coated composites subjected to blast loads. J Compos Mater2012; 46: 2167–2178.
21.
YanHOskayCKrishnanA. Compression after impact response of woven fiber-reinforced composites. Compos Sci Technol2010; 70: 2128–2136.
22.
CrouchROskayC. Accelerated time integrator for multiple time scale homogenization. Int J Numer Methods Eng2015; 101: 1019–1042.
23.
OskayCPalG. A multiscale failure model for analysis of thin heterogeneous plates. Int J Damage Mech2009; 19: 575–610.
24.
OskayC. Two-level multiscale enrichment methodology for modeling of heterogeneous plates. Int J Numer Methods Eng2009; 80: 1143–1170.
25.
KrishnanAOskayC. Modeling compression-after-impact response of polymer matrix composites subjected to seawater aging. J Compos Mater2012; 46: 2851–2861.
26.
BogdanorMJOskayCClaySB. Multiscale modeling of failure in composites under model parameter uncertainty. Comput Mech2015; 56: 389–404.
27.
Clay SB and Knoth PM. Experimental results of static testing for calibration and validation of composite progressive damage analysis methods. J Compos Mater 2016, in review.
28.
GuedesJMKikuchiN. Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng1990; 83: 143–198.
29.
DvorakGJ. Transformation field analysis of inelastic composite materials. Proc Roy Soc London1992; A437: 311–327.
30.
OskayCFishJ. Fatigue life prediction using 2-scale temporal asymptotic homogenization. Int J Numer Methods Eng2004; 61: 329–359.
31.
FishJYuQ. Computational mechanics of fatigue and life predictions for composite materials and structures. Comput Methods Appl Mech Eng2002; 191: 4827–4849.
32.
ASTM Standard 3518. Standard test method for in-plane shear response of polymer matrix composite materials by tensile test of a +/− laminate. ASTM International, West Conshohocken, PA, 2007.
33.
ASTM Standard 7078. Standard test method for shear properties of composite materials by v-notched rail shear method. ASTM International, West Conshohocken, PA, 2005.
34.
Song K, Li Y and Rose CA. Continuum damage mechanics models for the analysis of progressive failure in open-hole tension laminates. In: Proceedings of the 52nd AIAA Structures Structural Dynamics and Materials Conference, Denver, Colorado, 4–7 April 2011. American Institute of Aeronautics and Astronautics.
