A unified approach for variationally consistent finite elements in elastoplasticity Original Research Article

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 problem 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 variables’. The result is a set of non-linear algebraic equations, a subset of which can be interpreted as the backward-difference time-integrated ‘constitutive’ lawʹ of the finite element. An iterative procedure, where all calculations are at the element and not at the Gauss point level, resting on Newton-Raphson scheme is proposed for the solution of the governing equations. It is shown how the customary displacement approach and also some other mixed formulations in elastoplasticity can be regarded as special cases of the present formulation.