Analytical expression of mechanical fields for Gurson type porous models

Abstract

In this work, analytical expressions of mechanical fields are provided for strain hardening thermo-viscoplastic porous materials containing spheroidal voids subjected to homogeneous strain rate loading. Explicit relationships are provided for the macroscopic stress, the plastic multiplier, the effective equivalent plastic strain rate in the matrix when the constitutive behavior of the porous medium is of Gurson type model. Axisymmetric and non-axisymmetric loadings are considered. The behavior of the porous material is governed by the model developed by Gologanu et al. (Gologanu, M., Leblond, J.-B., Perrin, G., Devaux, J., 1997, CISM Courses and lectures,377, 61–130). The particular case of the Gurson model (Gurson, A. L., 1977, ASME Journal of Engineering Materials and Technology 99, 2–15) is also investigated since it is widely adopted in the literature for analytical modeling or finite elements calculations. Various matrix behaviors are considered. The matrix is first considered as rigid perfectly plastic. Interestingly, the approach is also valid for nonlinear viscoplastic material with work hardening and temperature dependency. Extensions are also considered when the matrix material is orthotropic. Finally, the numerical implementation is discussed and it is shown that by adopting the proposed approach, the efficiency of the radial return algorithm can be improved.