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# Mathematical Modelling and 3D FEM Analysis of the Influence of Initial Stresses on the ERR in a Band Crack’s Front in the Rectangular Orthotropic Thick Plate

Arzu Turan Dincel1, Surkay D. Akbarov2,3

Yildiz Technical University, Department of Mathematical Engineering, Davutpasa Campus, 34220, Esenler, Istanbul-Turkey.
Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering, Yildiz Campus, 34349, Besiktas, Istanbul-Turkey.
Institute of Mathematics and Mechanics of the National Academy of Science of Azerbaijan, 37041, Baku, Azerbaijan.

Computers, Materials & Continua 2017, 53(3), 249-270. https://doi.org/10.32604/cmc.2017.053.265

## Abstract

This paper deals with the mathematical modelling and 3D FEM study of the energy release rate (ERR) in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes. The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located. After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied. The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration. Numerical results on the influence of the initial stress, anisotropy properties of the plate material, the crack’s length and its distance from the face planes of the plate on the values of the ERR, are presented and discussed. In particular, it is established that for the relatively greater length of the crack’s band, the initial stretching of the plate causes a decrease, but the initial compression causes an increase in the values of the ERR.

## Keywords

A. Turan Dincel and S. D. Akbarov, "Mathematical modelling and 3d fem analysis of the influence of initial stresses on the err in a band crack’s front in the rectangular orthotropic thick plate," Computers, Materials & Continua, vol. 53, no.3, pp. 249–270, 2017.

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