Continuum damage accumulation model with a scalar damage function

Аuthors

Mohsen M. ^*, Rabinskiy L. N.^**, Egorova O. V.^***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: m.manoun93@gmail.com
**e-mail: rabinskiy@mail.ru
***e-mail: janus_olga@mail.ru

Abstract

This study presents a continuum damage accumulation model utilizing a scalar macro-parameter to describe the linear degradation of material properties. The deformation model for an elastic medium is formulated based on the Lagrange variational principle, with the damage parameter incorporated into the potential energy density function. This formulation yields a coupled, nonlinear boundary value problem, supplemented by an additional Euler equation governing the damage parameter evolution. A successive approximation method, analogous to the elastic solutions technique, is employed to solve the system. The model is validated through a one-dimensional rod tension problem. A comparative analysis of concentrated versus distributed loading conditions reveals a significant influence of the load type on the fracture pattern and damage distribution.

Keywords:

continuum damage mechanics; damage parameter; Lagrange variational principle; coupled boundary value problem; method of elastic solutions; fracture pattern

References

1. Dudchenko A.A., Lurie S.A. Modeling of damage growth and degradation of mechanical properties of layered composites. Moscow: MAI, 2019. 160 p. (In Russian)
2. Lurie S., Minhat M. Modeling of damage evaluation and failure of laminated composite materials across length scales. Cambridge, 2015. Pp. 143-196. URL: https://doi.org/10.1016/B978-0-08-100137-0.00007-9
3. Soutis C., Beaumont P.W.R. (Eds.). Multi-scale modeling of composite material systems: The art of predictive damage modeling. Woodhead Publishing Ltd, Cambridge, 2005.
4. Uhl K.M., Lucht B., Jeong H., Hsu D.K. Mechanical strength degradation of graphite fiber reinforced thermoset composites due to porosity. Review of Progress in Quantitative Nondestructive Evaluation, 1988. Pp. 1075-1082.
5. Lurie S.A., Belov P.A., Ozherelkov D.A. Modeling of damage to mechanical properties of materials in generalized gradient elasticity theory. In: Proceedings of the International Scientific Symposium on Problems of Mechanics of Deformable Bodies (Moscow, January 20-21, 2021). Moscow, 2021. Pp. 270-276. (In Russian)
6. Ovchinsky A.S. Failure and fracture processes in composite materials. Moscow: Nauka, 1988. 276 p. (In Russian)
7. Movchan A.A. Micromechanical approach in the problem of describing the accumulation of anisotropic scattered damage. Mechanics of Solids, 1990, no. 3, pp. 115-123. (In Russian)
8. Movchan A.A. Problems of strength of thin-walled structures. Moscow: MAI Publ., 1989. Pp. 20-24. (In Russian)
9. Doan Chuck Luat, Lurie S.A., Dudchenko A.A. Modeling of degradation of the composite properties on cracking and delamination when subjected to static and cyclic loading. Composites: Mechanics, Computations, Applications, An International Journal, 2010, vol. 1, no. 1, pp. 1-19.
10. Kashtalyan M., Soutis C. Analysis of composite laminates with intra- and interlaminar damage. Progress in Aerospace Sciences, 2005, vol. 41, pp. 152-173.
11. Vasiliev V.V., Morozov E.V. Advanced Mechanics of Composite Materials and Structural Elements. 3rd ed. Elsevier, 2013. 833 p.
12. Chang F.K., Chang K.Y. A progressive damage model for laminated composites containing stress concentrations. Journal of Composite Materials, 1987, vol. 21, no. 9, pp. 834-855.
13. Morozov E.V., Chen J.F., Shankar K. Computational modelling of progressive failure of composite materials and structures including plasticity effects. In: Proceedings of the XI International Conference on Computational Plasticity. Fundamentals and Applications (COMPLAS 2011). Barcelona, Spain, September 7-9, 2011.
14. Pinho S.T. Modelling failure of laminated composites using physically-based failure models. PhD thesis. London, UK: Department of Aeronautics, Imperial College, 2005.
15. Van Der Meer F.P., Sluys L.J. Continuum models for the analysis of progressive failure in composite laminates. Journal of Composite Materials, 2009, vol. 43, no. 20, pp. 2131-2156.
16. Placidi L., Misra A., Barchiesi E. Simulation results for damage with evolving microstructure and growing strain gradient moduli. Continuum Mechanics and Thermodynamics, 2019. URL: https://doi.org/10.1007/s00161-018-0693-z
17. Misra A., Singh V. Micromechanical model for viscoelastic materials undergoing damage. Continuum Mechanics and Thermodynamics, 2013, vol. 25, no. 2-4, pp. 343-358.
18. Placidi L. A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model. Continuum Mechanics and Thermodynamics, 2016, vol. 28, no. 1-2, pp. 119-137.
19. Krasnov M.L., Makarenko G.I., Kiselev A.I. Calculus of variations. Moscow: Main Editorial Board for Physical and Mathematical Literature, Nauka Publ., 1973. 190 p. (In Russian)
20. Petrov V.V. Nonlinear incremental structural mechanics. Moscow: Infra-Engineering, 2014. 480 p. (In Russian)

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