Archive of Applied Mechanics

, Volume 87, Issue 6, pp 1037–1048 | Cite as

Delamination fracture in a functionally graded multilayered beam with material nonlinearity



The present paper describes a theoretical study of delamination fracture in the functionally graded multilayered Crack Lap Shear (CLS) beam configuration with taking into account the nonlinear material behaviour. The fracture was analysed in terms of the strain energy release rate. The analytical solution derived is applicable for CLS with an arbitrary number of layers. Also, the delamination crack may be located arbitrary along the beam height. The mechanical behaviour of beam layers was modelled by a power-law stress–strain relation. It was assumed that the material in each layer is functionally graded along the thickness. Also, the material properties may be different in each layer. An analytical solution of the J-integral was derived in order to verify the nonlinear strain energy release rate analysis. The effects were evaluated of material gradient, crack location along the beam height and material nonlinearity on the strain energy release rate. It was shown that the analysis developed is a useful tool for the understanding of delamination fracture behaviour of functionally graded multilayered CLS beam configurations with material nonlinearity.


Functionally graded multilayered beam Fracture Material nonlinearity Analytical solution 



The present study was supported financially by the Research and Design Centre (CNIP) of the UACEG, Sofia (Contract BN–189/2016).


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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Technical MechanicsUniversity of Architecture, Civil Engineering and GeodesySofiaBulgaria

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