Variational formulations in the non-associated flow theory of plasticity
详细信息 查看全文
文摘
The theory proposed in Brun et al. [Brun, M. Carini, F. Genna, J. Mech. Phys. Solids 49(4) (2001) 839.], to construct simple variational formulations to any nonlinear problem, is applied to the case of the non-associated flow theory of plasticity. The relevant equations are written as a Linear Complementarity Problem (LCP), and include inequality and orthogonality constraints. This work starts by illustrating how the general theory discussed in Brun et al. (loc.cit.) must be particularized to the non-trivial case of a non-symmetric LCP. The obtained results are then applied to the rate plasticity equations, both at the material level and at the full boundary value problem level. Next, the case of the finite elastic–plastic problem is tackled. This problem does not admit a variational formulation even in the simple case of associated plasticity; this paper shows how the theory proposed in Brun et al. (loc.cit.) can be used to obtain min–max formulations for this case.