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This article treats the efficient solution of the linear syst ems of equations which arise during the iterative process within the finite element analysis of inelastic structures. Up to 80% of the total computation time is spend by the linear solver which suggests investigating this process. To this end high order time integration methods, diagonally implicit Runge-Kutta methods (DIRK), in combination with an inexact Multilevel-Newton algorithm (MLNA) are applied. Copyright line will be provided by the publisher 1 Constitutive Model In many engineering applications inelastic material properties such as plastic or viscous effects play a crucial role. These applications lead to nonlinear initial boundary value prob lems. In the case of isothermal quasi-static processes thes e consist of the local balance of linear momentum, suitable initial conditions for the displacement field and the velocity field as w ell as geometric and dynamic boundary conditions. The material can be described by constitutive models of evolutionary type. There the materials state is given by internal variables q, which develop according to either ordinary differential e quations or differential-algebraic equations (DAE) A u q = r(q, t). In the present paper the material model describes small strain viscoplasticity of the polymer polyoxmethylene. The model is based on an additive decomposition of the linearized Green strain tensor E = Ee + Ev into an elastic Ee and viscous Ev part. This ansatz and further assumptions yield the Cauchy stress tensor T = T e + T h + Tov = h(E, T h , Ev) as a sum of an equilibrium part with T h and without T e = T e(E) hysteresis and an overstress part Tov = Tov(Ee). Here the internal variables develop according to u Ev = 1 Tov and u |
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