Multiple methods exist for simulating crack propagation in the finite element method (FEM). Among these, the extended finite element method (XFEM) shows great potential as it allows for the use of larger elements while maintaining accuracy and practicality. Within XFEM, the employment of traction separation laws (TSLs) is a promising approach to capture post-necking effects, which are typically predicted poorly with larger elements. These TSLs are often assumed to be constant along the crack length and are determined by fitting to experimental data.

However, it has been proven that necking and fracture both depend on the state of stress, expressed as stress triaxiality. It is also known that the stress triaxiality within the crack region varies as the crack progresses through a plate due to changing boundary conditions and crack blunting. Consequently, the necking behaviour ahead of the crack tip changes, necessitating multiple stress state-dependent TSLs along the crack length to capture this effect accurately.

In this thesis, a subroutine is developed to enable the use of multiple TSLs along an extending crack in Abaqus based on the stress triaxiality of each element. Additionally, the relationship between TSL parameters and stress triaxiality was determined by minimizing the difference between simulations and experimental data of a large-scale CCT experiment. With this relationship known, it is possible to account for the effect of the changing stress state when determining the TSLs.

The study finds that stress triaxiality-dependent TSLs produce a significantly better match with experimental results compared to a stress triaxiality invariant TSL. This underscores the importance of addressing stress-state dependency in TSL determination. The study also highlights that mesh size and material dependency on TSLs must be addressed so that these TSLs can be applied universally across different conditions.

Impacts on offshore installations and ships can cause strains at high rates. It is known that mild steel lower yield stress and hardening are strain rate dependent. Measuring this material behavior is not easy, as test results from many researchers, show heavy vibration. Vibration is normally referred to as ringing. This thesis aims at measuring stress-strain behavior of mild steel at intermediate strain rates between 100 𝑠 −1 and 500 𝑠 −1 with minimal vibration. Two major characteristics from stress-strain behavior in this research, are the lower yield stress and plastic tangent modulus. A comparison of public test results, showed a steel characteristic for transferring quasi-static stresses, to stresses at a desired strain rate. This characteristic has been used to transfer a quasi-static stressstrain curve to stress-strain curves at intermediate strain rates. This strain rate dependent material model is used in calculations. The test is modelled by means of an explicit finite element analysis. The analysis showed that adding a plastic hinge in the specimen, can reduce bending and vibration. The test setup is a drop tower, where the drop weight falls into a U-shaped specimen. Strains are measured in an elastically and plastically deforming area on the specimen. Stresses in the plastic area can be obtained from strains in the elastically deforming area. Strains are measured by means of digital image correlation. Stresses are compared with loads obtained from drop weight positions and consequent accelerations. Measured plastic strains compare well to predicted plastic strains. However, stresses from first tests show vibration in a range of 20 percent of the average stress or more. If such bending occurs, it is not exactly known where the average stress is. However, the amount and direction of bending can be obtained from the 3D position measurements. The bending investigation is only used to identify causes of ringing. With insight in bending and loads from two separate measurements, this test is considered to produce results that represent the material behavior of mild steel. A raw test result with a vibration range of 20 percent of the average stress, in the first test setup, shows the potential for obtaining raw measurements from a U-shaped specimen in a drop test.