On the yield functionals in Lagrangian stress space of elastic-plastic materials with inter.pdf

-1- On the yield functionals in Lagrangian stress space of elastic-plastic materials with internal constraints Fu Mingfu，Chen Liangsen Center for Engineering Mechanics, Nanchang University, Jiangxi Province, China (330031) E-mail：fmfu@, Abstract In the present paper it is shown that the elastic range in the second Piola-Kirchhoff stress space can be chosen in a hyperplane perpendicular to the direction p γ = ? ? C CC if the determinate stress response of the elastic-plastic material with simple internal constraints with the condition (2.30) is correctly chosen, otherwise, it is in general in a hypersurface and the normal flow rule by Il’yushin’s postulate will have an indeterminate part( [8]). The choice of determinate stress response is probable because of its indeterminacy ([1]). Therefore the yield functional should be a function of the second Piola-Kirchhoff stress lying in the hyperplane so that it is more simple and the back stress as the geometric center of the elastic range in general is inside the elastic range. Finally some examples are concerned. Keywords：Elastic-plastic materials Constitutive relations Internal constraints 1．Introduction Truesdell and Noll [10] assumed that for simple materials with simple constraints their stress responses can be divided into two part, i.e, the stress is the sum of determinate stress and reaction stress, the determinate stress is determined by the admissible deformation process and the reaction stress is work-powerless. For simple internal constraints, Carlson and Tortorelli[3] has proved that the reaction stress is work-powerless for hyperelasticity, Casey[2] for elasticity and Baesu and Casey [1] for Lagrangian elastic-plastic materials. Truesdell and Noll [10] also pointed out that the stress response functional for determinate stress has some indeterminacy. The normalization condition can remove this indeterminacy, as proved by Cohen and Wang [5] and Vianello [11] for elastic material