Issue 67

B.N. Fedulov et alii, Frattura ed Integrità Strutturale, 67 (2024) 311-318; DOI: 10.3221/IGF-ESIS.67.22

Elastic nonlinearity of composite material can be found for many moduli [4-6] and relations to model this effect were performed by many researchers [7-11]. For example, Hahn at al. [7] added fourth degree for shear stress component into complimentary energy to capture shear nonlinearity. Testa at al. [8] analyzed many stress components of an arbitrary degree in potential function to model fabric nonlinear deformations for biaxial loading. Yang at al. in their work [9] also used fourth degree polynomic function for stress components to describe complimentary energy for fabric material. Slovikov, S. V. et al. [10] introduced a linear decay of the stiffness during compression loading of longitudinal composites. Complex complimentary energy function with successful correlation was proposed by Obid at al. [11]. Their energy function was inspired by famous Ramberg-Osgood potential widely used for hyper-elastic materials. Nevertheless, the question about longitudinal nonlinearity of unidirectional composite material is not completely unrevealed in terms of mechanism of appearance in uniaxial experiments and modelling approaches. The idea to get properties for composite material using finite element modeling with RVE approach is promising. However, the use of conventional short periodicity cell does not predict stiffness difference in dependence of type of loading for longitudinal uniaxial case [12]. Analyzing nonlinearity of longitudinal stiffness of composite material one can found that to obtain accurate results, the defects, arising in the material during the manufacturing process, should be taken into account. Such a well-known defect as fiber waviness, can occur during the layout operations and curing process of the composite product. Waviness refers to the deviation of the fiber from rectilinearity. It is known, that fiber waviness significantly influences mechanical characteristics such as Young's modulus and compressive strength. A considerable amount of research is devoted to the problem of fiber waviness and its impact on composite properties [12-24]. This study aims to develop constitutive relations for the continuum model with taken into account longitudinal elastic nonlinearity of composite material. Second purpose of this research is to understand mechanism of this elastic nonlinearity of composite material. A special numerical experiment was conducted employing finite element modeling techniques. The simulation using large periodic cell with fiber waviness provides a good quality nonlinear loading curves which are used as input data for purposed continuum model. It was demonstrated the change in longitudinal stiffness of the AS4/8552 composite material under uniaxial compression in the fiber direction for subsequent waviness angles. The findings of this research hold the potential to provide valuable insights for engineering and materials science, with implications for the design and optimization of composite structures and components. odelling of composite material with several nonlinearity in chosen direction requires a change in the constitutive relations. Considering classical approach (1) in terms of complacencies with the extension of longitudinal coefficient 11 A to be dependent on 11  , makes us to get sureness that relations remain elastic. In other words we need to perform potential function for any dependence of   11 11 A  .   11 11 11 11 12 13 22 22 12 22 23 33 33 13 23 33 12 12 12 13 13 13 23 23 23 0 0 0 0 0 0 0 0 0 0 0 0 1/ 0 0 0 0 0 0 1/ 0 0 0 0 0 0 1/ A A A A A A A A A G G G                                                                         (1) M C ONTINUUM MODEL





Let us consider the complimentary energy in the following specific form:

1 2

  11 11  





12 22 A A  

13 33 11   )



12 11 A A A     22 22

23 33 22   )



f

Φ

((

(

(2)

2   

2

2

13    12

23



13 11 A A A     23 22

33 33 33   )

(

)

G G G

12

13

23

312