Issue56

K.C. Nehar et alii, Frattura ed Integrità Strutturale, 56 (2021) 203-216; DOI: 10.3221/IGF-ESIS.56.17

[18] Baaser, H. (2010). Development and Application of the Finite Element Method based on MatLab. Springer Science & Business Media. [19] Tekkaya, A.E. and Soyarslan, C. (2018). Finite Element Method. In: Int. Academy for Production Engineering, Chatti S., Tolio T. (eds) CIRP Encyc. of Prod. Eng. Springer, Berlin, Heidelberg. DOI:10.1007/978-3-642-35950-7_16699-3 [20] Xiao, J. (2018). Recycled aggregate concrete structures, Springer-Verlag Berlin Heidelberg, pp. 65–98. DOI: 10.1007/978-3-662-53987-3. [21] Babu, V. S., Mullick, A. K., Jain, K. K. and Singh, P. K. (2015). Strength and durability characteristics of high-strength concrete with recycled aggregate-influence of processing. J. of Sust. Cem.-Bas. Mat., 4(1), pp. 54-71. DOI: 10.1080/21650373.2014.976777. [22] Baron, J. (1997). Les additions normalisées pour béton, Ecole française du béton, édition Eyrolles. [23] Gorisse, D., Festa, J. (1998). Nouveau guide du béton et de ses constituants, Huitième édition, Edition Eyrolles, France. [24] Aïtcin, P.C. (2001). Bétons haute performance, Edition Eyrolles, Paris. [25] Revilla-Cuesta, V., Skaf, M., Faleschini, F., Manso, J. M. and Ortega-López, V. (2020). Self-compacting concrete manufactured with recycled concrete aggregate: An overview. Jour. of Clea. Produc., 262, pp. 121362. DOI: 10.1016/j.jclepro.2020.121362. [26] Masood, B., Elahi, A., Barbhuiya, S. and Ali, B. (2020). Mechanical and durability performance of recycled aggregate concrete incorporating low calcium bentonite. Constru. and Build. Mat., 237, pp. 117760. DOI: 10.1016/j.conbuildmat.2019.117760. [27] MATLAB (1984). Script language with a development environmental for numerical calcul, Version 16.0, MathWorks, California, United States.

A NNEX

FEM Modeling In order to model the concrete samples, the finite element approximation is used [12]. We consider a quadrilateral element (Fig. A.1) the element is defined by four nodes in natural coordinates ( ξ , η ). The coordinates are interpolated and given as follows [15]:

    4 4 1 1 i i i i N u v 



u

N v

(1)

i i

Where u , v represents the displacements fields at any point of the element and u i , v i ; the nodal displacements.

Figure A.1. Quadrilateral Q4 element in natural coordinates ( ξ , η ).

N i represents the standard interpolation functions which are given by:

1 4

     ( ) ( ) l

  

  (1 )(1 )

(2)

( , ) N l

1

1

1

1 4

     ( ) ( ) l

  

  (1 )(1 )

(3)

( , ) N l

2

2

1

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