Premium
Analytical elastic‐plastic analyses of a spherical shell subjected to hydrostatic tension based on a strain gradient model for plastic metals
Author(s) -
Enakoutsa Koffi
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400131
Subject(s) - materials science , hydrostatic stress , plasticity , hydrostatic equilibrium , mechanics , tension (geology) , length scale , spherical shell , porosity , shell (structure) , hydrostatic pressure , elasticity (physics) , levy–mises equations , stress (linguistics) , composite material , finite element method , physics , thermodynamics , ultimate tensile strength , stress intensity factor , fracture mechanics , linguistics , philosophy , quantum mechanics
The problem of a spherical shell made of an elastic‐plastic second gradient model for plastic materials and subjected to hydrostatic tension is considered. The elastic‐plastic second gradient model is a simplified version (porosity neglected) of a second gradient model for plastic porous metals developed, some years ago, by Gologanu, Leblond, Perrin and Devaux, so‐called GLPD model. The expressions of the velocity field as well as the ordinary and double stress components are determined for the cases where the spherical shell is modeled by a purely elastic, purely plastic, and elastic‐plastic GLPD models. As expected, the solution developed in each case (elastic, ideal‐plastic, and elastic‐plastic) reduces to that of the first gradient as a special case when the characteristic length scale the GLPD model involves is negligible. Our results allow comparisons between the newly developed solution and the classical elastic‐plastic solution for the same model problem; they also provide insights into the influence of the characteristic length scale on the newly developed solution.