A Methodology to Construct Approximate Constitutive Equations for Porous Rubber Elastic Materials

Abstract : The present paper makes use of methods from theory of ductile fracture, which was developed to prevent catastrophic failures of steel vessels, for example gas pipelines. A number of structures are made of porous materials, with elastic, isochoric matrix, or of such materials which may become porous when they are subjected to excessive mechanical loads. Predicting the behavior of such structures requires a continuous model which accounts well for porous materials. In the oil and gas industry context, fluid tightness sheaths or gaskets enter this category. Indeed, these constituents are often made of polymers and may become porous in case of rapid pressure drop. Forecast of their behavior in such circumstances, in particular global tightness forecast, calls for a continuous model accounting for porous materials behavior with sufficient accuracy. The aim of the present paper is to adapt a methodology from ductile fracture theory to construct such a model, through the analysis of a hollow sphere considered as a material Representative Volume Element (RVE). The mechanical problem is written under a variational form, within the framework of material elastic behavior. In the vicinity of the central void, large strains are encountered. The well-known Gurson theory [Gurson, A.L. (1977) J. Eng. Mater. - T. ASME, 99, 2-15] which was developed in the above mentioned context of steel ductile failure is adapted to provide an approximation of the macroscopic (RVE scale) stress tensor. This approximation constitutes the announced model. Computations are performed for one classical rubber elastic behavior (Neo-Hookean model), which is the simplest model combining elasticity and large strain. Finite Element Method computations show that the approximation is sufficiently tight.
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G. Perrin. A Methodology to Construct Approximate Constitutive Equations for Porous Rubber Elastic Materials. Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, Institut Français du Pétrole, 2006, 61 (6), pp.773-779. ⟨10.2516/ogst:2006016⟩. ⟨hal-02005888⟩

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