Julia Mergheim

Thermomechanical simulation of the selective laser melting process for PA12 including volumetric shrinkage

The present contribution is concerned with the finite element simulation of the thermomechanical material behavior in the selective laser melting process for PA12. In the process shrinkage of the powder material is observed when becoming melt, as the porous character of the powder vanishes due to the phase transition. A nonlinear thermomechanical finite element model is developed, which captures the shrinkage of the material and includes temperature dependent material parameters. The model is used to simulate the shrinkage of the material in the process, where an adaptive mesh refinement is applied for increasing the accuracy of the simulation. The results are qualitatively compared with experimental data and show a good agreement.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

Modeling and Simulation of Curing and Damage in Thermosetting Adhesives

The curing of thermosetting adhesives is a complex polymerization process that involves the transition of a viscous liquid into a viscoelastic solid. This phase transition is frequently accompanied by a volume shrinkage of the material, which may induce mechanical strains and stresses. These, in turn, can lead to a reduced performance or even failure of the adhesive joint. The present contribution introduces a continuum mechanical model that is suited to describe the emergence of stresses and the corresponding initiation of material degradation in adhesive layers, both during the process of curing and, of course, during subsequent loading. The model is implemented into a finite element code and some numerical examples demonstrate the interaction of curing shrinkage, stress evolution, and damage.

On the Application of Hansbo’s Method for Interface Problems

A geometrically nonlinear finite element framework for the modeling of strong discontinuities in three dimensional continua is presented. By doubling the degrees of freedom in the discontinuous elements, the algorithm allows for arbitrary discontinuities which are not a priori restricted to inter-element boundaries. On both sides of the discontinuity we apply an independent interpolation of the deformation field. Accordingly, the suggested approach relies exclusively on displacement degrees of freedom. On the discontinuity surface itself, we make use of the cohesive zone concept to account for a smooth crack opening. A three dimensional bending problem and the classical symmetric and non-symmetric peel test demonstrate the performance of the suggested method.

C 1 Discretizations for the Application to Gradient Elasticity

For the numerical solution of gradient elasticity, the appearance of strain gradients in the weak form of the equilibrium equation leads to the need for C 1-continuous discretization methods. In the present work, the performances of a variety of C 1-continuous elements as well as the C 1 Natural Element Method are investigated for the application to nonlinear gradient elasticity. In terms of subparametric triangular elements the Argyris, Hsieh–Clough–Tocher and Powell–Sabin split elements are utilized. As an isoparametric quadrilateral element, the Bogner–Fox–Schmidt element is used. All these methods are applied to two different numerical examples and the convergence behavior with respect to the L 2, H 1 and H 2 error norms is examined.

Simulation of the temperature distribution in the selective beam melting process for polymer material

In the present contribution the temperature distribution in the selective beam melting process for polymer materials is simulated to better understand the influence of process parameters on the properties of the produced part. The basis for the developed simulation tool is the nonlinear heat equation including temperature dependent functions for the heat capacity and the heat conduction which were obtained by experimental measurements. The effect of latent heat occurring in the process is also taken into account. The heat equation is discretized in time and space where a Runge-Kutta method of Radau IIA type is used for time integration. An adaptive finite element method is applied for the discretization in space and the model is implemented into the finite element library deal.II. The heat and cooling rate as important process parameters are simulated for different beam velocities. The ability for computing these process parameters makes the simulation tool suited for optimizing the process management of selective beam melting plants.

Computational Homogenization of Defect Driving Forces

Due to the fact that many engineering materials and also biological tissues possess an underlying (heterogeneous) micro-structure it is not sufficient to simulate these materials by pre-assumed overall constitutive assumptions. Therefore, we apply a homogenization scheme, which determines the macroscopic material behavior based on analysis of the underlying micro-structure. In the work at hand focus is put on the extension of the classical computational homogenization scheme towards the homogenization of material forces. Therefore, volume forces have to incorporated which may emerge due to inhomogeneities in the material. With assistance of this material formulation and the equivalence of the J-integral and the material force at a crack tip, studies on the influence of the micro-structure onto the macroscopic crack-propagation are carried out.