Steffen Rothe

Homogeneous stress---strain states computed by 3D-stress algorithms of FE-codes: application to material parameter identification

In view of code verification of finite element implementations and for material parameter identification purposes it is of interest to make use of stress algorithms developed for three-dimensional finite element computations. In the case of homogeneous deformations various boundary-conditions for given displacements or stresses are possible and define a sub-problem of three-dimensional stress–strain states, which are either one-, two- or three-dimensional. Examples are uniaxial tension/compression, plane stress conditions or biaxial tensile problems. Caused by the fact that the stress algorithms are strain-driven, the constraints of zero stresses in a specific direction lead for elastic and inelastic constitutive models to a particular system of differential-algebraic equations. How to treat such stress algorithms and how to solve the resulting system of differential-algebraic equations, which are developed for finite element programs, for specific stress and displacement boundary conditions is discussed in this article. Additionally, it is worked out that the consistent tangent operator is required in the same manner as in 3D-FE computations. The second topic treats the extension of the entire procedure for material parameter identification procedure applied to test data for different materials such as steel, rubber material and powder. In this respect, uniaxial tensile, biaxial tensile tests, and laterally constrained loading paths are exemplarily investigated. These investigations and the proposed procedure are applied for small and finite strain problems. In this investigation measure of the quality of identification is discussed as well.

Electro-Thermo-Elastic Simulation of Graphite Tools Used in SPS Processes

In the range of field-assisted sintering technology or spark plasma sintering all materials in the testing machine undergo very large temperature changes. The powder material, which has to be sintered, is filled into a graphite die and mechanically loaded by a graphite punch. The heat is produced by electrical induction and the cooling process is performed by conduction and radiation. Both the heating and the cooling process are very fast. In order to understand the process of the highly loaded graphite parts, experiments, modeling and computations have to be carried out. On the thermal side the temperature-dependent material properties such as heat capacity and heat conductivity have to be modeled. Since the heat capacity is not independent of the Helmholtz free-energy a particular consideration of the free-energy is carried out. On the other hand, the temperature changes of the electrical resistivity and the material properties of the graphite tool must be taken into considerations. Accordingly, the material properties of “Ohm’s law” must be modeled as well. The fully coupled system comprising the electrical, thermal and mechanical field are solved numerically by a monolithic finite element approach. After the spatial discretization using finite elements one arrives at a system of differential-algebraic equations which is solved by means of diagonally implicit Runge-Kutta methods. Issues and open questions in the numerics are addressed and problems in modeling a real application are discussed.

A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis

In this essay the rigorous application of the method of vertical lines, i.e. performing the successive steps of spatial and temporal discretization is investigated for dynamical and quasi-statical systems. A particular focus lies in the field of solid mechanics where constitutive models of evolutionary-type are of basic interest. Various coupled systems, i.e. thermo-mechanical, electro-thermal or electro-thermo-mechanical coupled problems are investigated in view of the structure of their resulting equations, commonly, leading to systems of ordinary differential equations or systems of differential-algebraic equations after the spatial discretization step. For the case of a thermo-mechanical and an electro-thermal problem stiffly accurate diagonally-implicit Runge-Kutta methods are applied.