Generalized variable finite element modeling and extremum theorems in stepwise holonomic elastoplasticity with internal variables

Abstract Reference is made to a broad class of elastic-plastic constitutive laws with internal variables (occuring in pairs of conjugate kinematic and static quantities). Their Euler backward-difference, ‘stepwise-holonomic’ formulation is derived for the time discretization of initial-boundary value problems. The space discretization is performed by systematically using the notion of ‘generalized variables’ and by generating overall, average constitutive laws for finite elements (instead of enforcing the material model in some points). Some categories of finite element models in generalized variables are comparatively discussed. Two pairs of dual extremum characterizations of the solution to the boundary value problem for a finite load step are established.

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