A UNIFIED APPROACH FOR VARIATIONALLY CONSISTENT FINITE-ELEMENTS IN ELASTOPLASTICITY

A general, variationally consistent approach for elastoplastic finite element analysis is presented. A weak formulation of the finite-step ( i.e. in terms of finite increments) elastoplastic boundary value probl em is obtained by enforcing the stationarity of a mixed functional of Hu-Washizu type. A peculiarity of the present formulation is that the constitutive equations are expressed in weak form also. All fields are then independently discretized in terms of so-called 'generalized var iables'. The result is a set of non-linear algebraic equations, a subs et of which can be interpreted as the backward-difference time-integra ted 'constitutive law' of the finite element. An iterative procedure, where all calculations are at the element and not at the Gauss point l evel, resting on Newton-Raphson scheme is proposed for the solution of the governing equations. It is shown how the customary displacement a pproach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation.