Issue 51

R. Massabò et alii, Frattura ed Integrità Strutturale, 51 (2020) 275-287; DOI: 10.3221/IGF-ESIS.51.22

[18] Massabo, R, Darban, H. (2019). Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach, Eng. Fract. Mech., 213, pp. 280–301, DOI: 10.1016/j.engfracmech.2019.03.002. [19] Pelassa, M., Massabò, R. (2015). Explicit solutions for multi-layered wide plates and beams with perfect and imperfect bonding and delaminations under thermo-mechanical loading, Meccanica, 50(10), pp. 2497–2524, DOI: 10.1007/s11012-015-0147-7. [20] Darban, H., Massabò, R. (2018). A homogenized structural model for shear deformable composites with compliant interlayers, Multiscale Multidiscip. Model. Exp. Des., 1, pp. 269–290, DOI: 10.1007/s41939-018-0032-x. [21] Massabò, R. (2017). Propagation of Rayleigh-Lamb waves in multilayered plates through a multiscale structural model, Int. J. Solids Struct., 124, pp. 108–124, DOI: 10.1016/j.ijsolstr.2017.06.020. [22] Massabò, R. (2014). Influence of boundary conditions on the response of multilayered plates with cohesive interfaces and delaminations using a homogenized approach, Frat. Ed Integrita Strutt., 8(29), pp. 230–240, DOI: 10.3221/IGF-ESIS.29.20. [23] Andrews, M.G., Massabò, R. (2007). The effects of shear and near tip deformations on energy release rate and mode mixity of edge-cracked orthotropic layers, Eng. Fract. Mech., 74(17), pp. 2700–2720, DOI: 10.1016/j.engfracmech.2007.01.013. [24] Madhukar, M.S., Drzal, L.T. (1992). Fiber-matrix adhesion and its effect on composite mechanical properties: IV. mode I and mode II fracture toughness of graphite/epoxy composites, J. Compos. Mater., 26(7), pp. 936–968, DOI: 10.1177/002199839202600701. [25] Monetto, I., Campi, F. (2017). Numerical analysis of two-layer beams with interlayer slip and step-wise linear interface law, Eng. Struct., 144, pp. 201–209, DOI: 10.1016/j.engstruct.2017.04.010. [26] Suo, Z., Bao, G., Fan, B., Wang, T.C. (1991). Orthotropy rescaling and implications for fracture in composites, Int. J. Solids Struct., 28(2), pp. 235–248, DOI: 10.1016/0020-7683(91)90208-W. [27] Ustinov, K.B., Massabò, R., Lisovenko, D.S. (2019). Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip. Analytical solution, Submitted. [28] Tawk, I., Navarro, P., Ferrero, J.F., Barrau, J.J., Abdullah, E. (2010). Composite delamination modelling using a multi layered solid element, Compos. Sci. Technol., 70(2), pp. 207–214, DOI: 10.1016/j.compscitech.2009.10.008. [29] Kim, H.S., Chattopadhyay, A., Ghoshal, A. (2003). Characterization of delamination effect on composite laminates using a new generalized layerwise approach, Comput. Struct., 81(5), pp. 1555–1566, DOI: 10.1016/S0045-7949(03)00150-0. [30] Flores, F.G., Oller, S., Nallim, L.G. (2018). On the analysis of non-homogeneous laminates using the refined zigzag theory, Compos. Struct., 204, pp. 791–802, DOI: 10.1016/j.compstruct.2018.08.018. [31] Massabò, R. (2019). Mixed-mode delamination in layered beams using a homogenized structural approach, internal report. University of Genova, Italy.

A PPENDIX

Relevant constitutive, equilibrium and compatibility equations in layer k :

; ( ) k

;

( ) k

( ) k

( ) k

( ) k

( ) k













C

G

2

22

22

22

23

23

23

( ) k

( ) k







0  ;

,

,

(7)

22 2

23 3

  k

 

;   2 k

  k

  k

k v

22  

23 2 3    , v

v

2 2 ,

,

3 2

Force and moment resultants:

n x





3 k







ˆ 

b

( ) k

b

z

zS



2 2 g 22 2 2 Q x Q x Q x M x    ( ) ( ) ( ) , ( ) 2 2 2 2





, N M

x dx

( ) x

1,

;

(8)

22 22

22

3

3

2 2



3 k

1

x



k

1

with:

286