Charlotte Kuhn

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distinguishes between broken and undamaged material. At crack faces the order parameter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time integration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture models are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investigates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to experimental data.

Configurational Forces in a Phase Field Model for Dynamic Brittle Fracture

In this work, the concept of configurational forces is proposed to enhance the post-processing of phase field simulations for dynamic brittle fracture. A local configurational force balance is derived by taking the gradient of the Lagrangian density of the phase field fracture problem. It is shown that the total configurational forces computed for a crack tip control volume are closely related to the Griffith criterion of classical fracture mechanics. Finally, the evaluation of the configurational within the finite element framework is demonstrated by two examples.

Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state

Recently, an equation of state (EoS) for the Lennard-Jones truncated and shifted (LJTS) fluid has become available. As it describes metastable and unstable states well, it is suited for predicting density profiles in vapor-liquid interfaces in combination with density gradient theory (DGT). DGT is usually applied to describe interfaces in Cartesian one-dimensional scenarios. In the present work, the perturbed LJ truncated and shifted (PeTS) EoS is implemented into a three-dimensional phase field (PF) model which can be used for studying inhomogeneous gas-liquid systems in a more general way. The results are compared with the results from molecular dynamics simulations for the LJTS fluid that are carried out in the present work and good agreement is observed. The PF model can therefore be used to overcome the scale limit of molecular simulations. A finite element approach is applied for the implementation of the PF model. This requires the first and second derivatives of the PeTS EoS which are calculated using hyper-dual numbers. Several tests and examples of applications of the new PeTS PF model are discussed.

Numerical homogenization of the Eshelby tensor at small strains

Numerical homogenization methods, such as the FE2 approach, are widely used to compute the effective physical properties of microstructured materials. Thereby, the macroscopic material law is replaced by the solution of a microscopic boundary value problem on a representative volume element in conjunction with appropriate averaging techniques. This concept can be extended to configurational or material quantities, like the Eshelby stress tensor, which are associated with configurational changes of continuum bodies. In this work, the focus is on the computation of the macroscopic Eshelby stress tensor within a small-strain setting. The macroscopic Eshelby stress tensor is defined as the volume average of its microscopic counterpart. On the microscale, the Eshelby stress tensor can be computed from quantities known from the solution of the physical microscopic boundary value problem. However, in contrast to the physical quantities of interest, i.e. stress and strain, the Eshelby stress tensor is sensitive to rigid body rotations of the representative volume element. In this work, it is demonstrated how this must be taken into account in the computation of the macroscopic Eshelby stress tensor. The theoretical findings are illustrated by a benchmark simulation and further simulation results indicate the microstructural influence on the macroscopic configurational forces.

Numerical Solution Strategies for a Dynamic Phase Field Fracture Model

This work discusses the efficiency of six strategies for the numerical solution of the coupled system of partial differential equations that arise from a phase field description of dynamic fracture. Efficient numerical treatment of the dynamic phase field fracture model is a prerequisite for the simulation of failure due to brittle fracture in realistic scenarios such as manufacturing.Firstly, the phase field description of fracturing of brittle solids is introduced. Afterwards, three monolithic as well as three staggered finite element solution strategies are outlined and their performance is studied in two benchmark problems.

Modeling of the Effective Properties of Metal Matrix Composites Using Computational Homogenization

On the macrolevel metal matrix composites (MMCs) resemble a homogeneous material. However, on the microlevel they have an inhomogeneous microstructure. This paper will show how heterogeneities affect the effective macroscopic properties the material, i.e. the effective properties. This investigation is done using computational homogenization techniques. Finite element (FE) simulations were conducted in ABAQUS in combination with MATLAB, using material parameters for aluminum alloy AA2124 and silicon carbide SiC to develop a representative volume element (RVE) of the MMC AMC217xe.