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In the present paper a multifield approach towards ideal elastoplasticity is presented and its numerical implementation is touched. Furthermore, the strategy of static condensation is applied to this ansatz. With the help of an axisymmetric model problem its realization is demonstrated and compared to the pure multifield approach. MotivationDifferent industrial manufacturing processes are characterized by plastic deformations where dynamic effects cannot be longer neglected, cf. [6]. Thus, the analysis of time discretization schemes linked to plasticity comes to the fore. In this context alternative numerical implementations have to be taken into account and optimized with regard to their computational effort. In order to carry out the time discretization of an elastoplastic problem in one single step a multifield approach will be introduced and examined. Multifield formulation of elastoplasticityIn order to describe elastoplastic deformation processes mathematically, adequate equations have to be derived. Within the framework of a multifield approach this can be done by formulating the balance of power augmented by a dissipation potential, cf. [2]. The latter characterizes the occurring plastic effects. Furthermore, it is assumed that the physical state, where the virtual power reaches a stationary point, is the preferable one. Consequently, an enhanced version of the principle of JOURDAIN is exploited leading to δP = δĖ + δK + δẆ + δD = 0.(1)Therein δĖ represents the internal virtual power, δK the virtual power of inertia effects, δẆ the power due to external forces and δD the virtual dissipation potential. Following the approach in [5] and references therein the nonlinear system of equations can be derived, assuming that δγ ≥ 0 and f (σ) ≤ 0 hold.

The present paper considers the spread of longitudinal waves in an elastic rod. On the one hand an analytical solution is presented, on the other hand a spatially and temporally discretized continuum formulation of this problem is treated. With these approaches at hand the appearing time discretization error is analyzed using various quantities.

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