On modelling damage in composite laminates using the Ritz method and continuum damage mechanics
Dario Campagna, Alberto Milazzo, Vincenzo Oliveri, Ivano Benedettidownload PDF
Abstract. In this work, a Ritz formulation for the analysis of damage initiation and evolution in composite plates under progressive loading is presented. The proposed model assumes a first order shear deformation theory and considers geometric non-linearities through the von Karman assumptions. The damage is modelled through Continuum Damage Mechanics. A set of results is presented to show the potential of the method and highlight some issues to be addressed by suitable developments of the method.
Ritz Method, Continuum Damage Mechanics, Gibbs Effect, Variable Angle Tow Laminates
Published online 9/1/2023, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Dario Campagna, Alberto Milazzo, Vincenzo Oliveri, Ivano Benedetti, On modelling damage in composite laminates using the Ritz method and continuum damage mechanics, Materials Research Proceedings, Vol. 33, pp 233-238, 2023
The article was published as article 34 of the book Aerospace Science and Engineering
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 Z. Gürdal and R. Olmedo, In-plane response of laminates with spatially varying fiber orientations – Variable stiffness concept, AIAA J. 31, 4 (1993) 751–758. https://doi.org/10.2514/3.11613.
 Z. Gürdal, B. Tatting, and C. Wu, Variable stiffness composite panels: Effects of stiffness variation on the in-plane and buckling response, Compos. A: Appl. Sci. Manuf 39, 5 (2008) 911–922. https://doi.org/10.1016/j.compositesa.2007.11.015.
 M. Lo Cascio and I. Benedetti, Coupling BEM and VEM for the analysis of composite materials with damage, J. Multiscale Modell. 13, 01 (2022) 2144001. https://doi.org/10.1142/S1756973721440017.
 A. Matzenmiller, J. Lubliner, and R. Taylor, A constitutive model for anisotropic damage in fiber-composites, Mech. Mater. 20, 2 (1995) 125–152. https://doi.org/10.1016/0167-6636(94)00053-0.
 P. Ladeveze and E. LeDantec, Damage modelling of the elementary ply for laminated composites, Compos. Sci. Technol., 43, 3 (1992) 257–267. https://doi.org/10.1016/0266-3538(92)90097-M.
 P. Maimí, P. Camanho, J. Mayugo, and C. Dávila, A continuum damage model for composite laminates: Part I – constitutive model, Mech. Mater. 39, 10 (2007) 897–908. https://doi.org/10.1016/j.mechmat.2007.03.005.
 P. Maimí, P. Camanho, J. Mayugo, and C. Dávila, A continuum damage model for composite laminates: Part II – computational implementation and validation, Mech. Mater. 39, 10 (2007) 909–919. https://doi.org/10.1016/j.mechmat.2007.03.006.
 D. Campagna, A. Milazzo, I. Benedetti, and V. Oliveri, A non-linear Ritz method for progressive failure analysis of variable angle tow composite laminates, Mech. Adv. Mater. Struc. (2022). https://doi.org/10.1080/15376494.2022.2134951.
 I. Benedetti, H. Nguyen, R. A. Soler-Crespo, W. Gao, L. Mao, A. Ghasemi, … and H. D. Espinosa. Formulation and validation of a reduced order model of 2D materials exhibiting a two-phase microstructure as applied to graphene oxide. J Mech Phys Solids 112 (2018) 66-88. https://doi.org/10.1016/j.jmps.2017.11.012
 M. Jirásek and D. Rodrigue, Localization analysis of nonlocal models with damage-dependent nonlocal interaction. Int J Solids Struct 174 (2019) 1-17. https://doi.org/10.1016/j.ijsolstr.2015.06.001
 Q. J. Yang and B. Hayman, Simplified ultimate strength analysis of compressed composite plates with linear material degradation, Compos. B: Eng. 69 (2015) 13–21 https://doi.org/10.1016/j.compositesb.2014.09.016.
 Q. J. Yang and B. Hayman, Prediction of post-buckling and ultimate compressive strength of composite plates by semi-analytical methods, Eng. Struct. 84 (2015) 42–53. https://doi.org/10.1016/j.engstruct.2014.11.013.
 Z. Hashin and A. Rotem, A fatigue failure criterion for fiber reinforced materials, J. Compos. Mater. 7, 4 (1973) 448–464. https://doi.org/10.1177/002199837300700404.
 M.H. Nagaraj, J. Reiner, R. Vaziri, E. Carrera, and M. Petrolo, Progressive damage analysis of composite structures using higher-order layer-wise elements, Compos Part B-Eng 190 (2020) 107921. https://doi.org/10.1016/j.compositesb.2020.107921.
 A. Milazzo and V. Oliveri, Buckling and Postbuckling of Stiffened Composite Panels with Cracks and Delaminations by Ritz Approach, AIAA J. 53, 3 (2017) 965-980. https://doi.org/10.1016/j.ijsolstr.2018.10.002.
 V. Oliveri and A. Milazzo, A Rayleigh-Ritz approach for postbuckling analysis of variable angle tow composite stiffened panels, Comput. Struct. 196 (2018) 263-276. https://doi.org/10.1016/j.compstruc.2017.10.009.