Abstract
This article is relevant, as changes during the external loading may affect the stress state of the materials. The aim of this paper is to consider the numerical modeling of heating for circular cylinders in the frame of the theory of elastic materials with voids. A numerical solution is build using COMSOL Multiphysics software, where the implementation of the considered theory is realized based on the direct equation-definition approach. Constitutive relations were written in General form partial differential equation module. A matrix form of the equations for the two-dimensional case was used. Scale effects arising in considered problems are discussed. The classical solution is the particular case of the considered theory, when the coupling number tends to asero, i.e. when the micro-dilatation effects are small and do not affect the material's stress state. The limiting case in the case of the small value of the coupling number is the classical thermoelasticity solution.
Highlights
Elasticity with voids theory was presented in [1]
Presented in this paper numerical solution for the pressurized thick-walled cylinder can be used for the validation of the micro-dilatation effects been identified in the experimental test with micro-tubes made of porous materials, such as ceramics or some type of polymers
The presented solution describes the behavior of the structure with micro-dilatation, i.e. with valuable changes of porosity under external loading that affects the material stress state
Summary
Elasticity with voids theory was presented in [1]. Linear approximation of this theory was presented in [2]. The same model was proposed in the paper [3]. It can be considered as a simplified model of the Mindlin continuum [4]. The problem for the plate with a hole was solved in the paper [5]. In paper [7] it was shown that within the framework of the elasticity with voids theory, there is no polynomial solution similar to the classical solution of the Saint-Venant problem
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