On the behaviour of spherical inclusions in a cylinder under tension loads

Ingenius
Vol. 19, 2018, pp. 69-78

S. Montero, R. Bustamante, A. Ortiz-Bernardin

Abstract

In the present paper the behaviour of a hyperelastic body is studied, considering the presence of one, two and more spherical inclusions, under the effect of an external tension load. The inclusions are modelled as nonlinear elastic bodies that undergo small strains. For the material constitutive relation, a relatively new type of model is used, wherein the strains (linearized strain) are assumed to be nonlinear functions of the stresses. In particular, a function is used that keeps the strains small, independently of the magnitude of the external loads. In order to simplify the problem, the hyperelastic medium and the inclusions are modelled as axial-symmetric bodies. The finite element method is used to obtain results for these boundary value problems. The objective of using these new models for elastic bodies in the case of the inclusions is to study the behaviour of such bodies in the case of concentration of stresses, which happens near the interface with the surrounding matrix. From the results presented in this paper, it is possible to observe that despite the relatively large magnitude for the stresses, the strains for the inclusions remain small, which would be closer to the actual behaviour of real inclusions made of brittle materials, which cannot show large strains.

Keywords: nonlinear elasticity; strain limiting behavior; finite element method; constitutive equations; elastic bodies; isotropic bodies.

Original Journal Article (Free – Open Access): https://revistas.ups.edu.ec/index.php/ingenius/article/view/19.2018.07

 

Publications by Alejandro Ortiz-Bernardin