Eventos Anais de eventos
MECSOL 2019
7th International Symposium on Solid Mechanics
An extended Gurson model based approach for constitutive modeling of orthotropic porous solids
Submission Author:
Ayrton Ribeiro Ferreira , SP
Co-Authors:
Ayrton Ribeiro Ferreira, Sergio Persival Proenca, Ahmed BENALLAL
Presenter: Ayrton Ribeiro Ferreira
doi://10.26678/ABCM.MECSOL2019.MSL19-0036
Abstract
The paper is concerned with the derivation of the effective behavior of anisotropic porous materials, aiming to better represent such materials at failure conditions when subjected to arbitrary stress states. This derivation is based on the acclaimed Gurson model widely recognized as an adequate isotropic framework to model both plasticity and damage evolution for ductile porous materials. The Gurson model is obtained through an upper bound limit analysis on a spherical Representative Volume Element (RVE) with a centered spherical void by prescribing a specific trial velocity field to its domain with such special properties that facilitates the analytical deriving of the effective yield criterion. In this way, the purpose of this work is to extend the Gurson model for porous materials with orthotropic matrix. The orthotropic behaviour of the matrix is an extension of isotropic models taking into account the influence of the second and third stress invariants on the matrix yielding law, following the Hershey-Dalgreen-Hosford (HDH) criterion. All the pores throughout this work are geometrically assumed to be spherical. Therefore, there is no morphological effect on the anisotropy considered here and only the anisotropic yielding of the matrix is considered. Due to the complexity of the new features of this Gurson Model extension, not detailed hereby, the effective yield criterion expressions are presented in a non-closed form. Therefore, for a better understanding of the model response some numerical analyses are then required to illustrate the obtained results. The analyses can be described in two main steps: 1) Firstly, the tensorial direction of the macroscopic strain rate field (E) is varied in the whole range of validity and then the macroscopic stress tensor response for each applied E is computed by using the non-closed expressions of the criterion; 2) In order to properly visualize the yield surface, contour plots of the orthotropic yield surface in planes of interest, as the deviatoric and meridional ones are constructed. The results hereby presented are related to porous materials with different matrix properties, in correspondence to a variation of the HDH coefficients. One concludes about the usefulness of the model as well as its comprehensiveness to include materials with unusual orthotropic parameters.
Keywords
Porous media, Gurson Model, orthotropy, Constitutive modeling, ductile fracture
