Ton van den Boogaard

A comparison between dynamic implicit and explicit finite element simulations of the native knee joint

The finite element (FE) method has been widely used to investigate knee biomechanics. Time integration algorithms for dynamic problems in finite element analysis can be classified as either implicit or explicit. Although previously both static/dynamic implicit and dynamic explicit method have been used, a comparative study on the outcomes of both methods is of high interest for the knee modeling community. The aim of this study is to compare static, dynamic implicit and dynamic explicit solutions in analyses of the knee joint to assess the prediction of dynamic effects, potential convergence problems, the accuracy and stability of the calculations, the difference in computational time, and the influence of mass-scaling in the explicit formulation. The heel-strike phase of fast, normal and slow gait was simulated for two different body masses in a model of the native knee. Our results indicate that ignoring the dynamic effect can alter joint motion. Explicit analyses are suitable to simulate dynamic loading of the knee joint in high-speed simulations, as this method offers a substantial reduction of the computational time with a similar prediction of cartilage stresses and meniscus strains. Although mass-scaling can provide even more gain in computational time, it is not recommended for high-speed activities, in which inertial forces play a significant role.

The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint

In finite element (FE) models knee ligaments can represented either by a group of one-dimensional springs, or by three-dimensional continuum elements based on segmentations. Continuum models closer approximate the anatomy, and facilitate ligament wrapping, while spring models are computationally less expensive. The mechanical properties of ligaments can be based on literature, or adjusted specifically for the subject. In the current study we investigated the effect of ligament modelling strategy on the predictive capability of FE models of the human knee joint. The effect of literature-based versus specimen-specific optimized material parameters was evaluated. Experiments were performed on three human cadaver knees, which were modelled in FE models with ligaments represented either using springs, or using continuum representations. In spring representation collateral ligaments were each modelled with three and cruciate ligaments with two single-element bundles. Stiffness parameters and pre-strains were optimized based on laxity tests for both approaches. Validation experiments were conducted to evaluate the outcomes of the FE models. Models (both spring and continuum) with subject-specific properties improved the predicted kinematics and contact outcome parameters. Models incorporating literature-based parameters, and particularly the spring models (with the representations implemented in this study), led to relatively high errors in kinematics and contact pressures. Using a continuum modelling approach resulted in more accurate contact outcome variables than the spring representation with two (cruciate ligaments) and three (collateral ligaments) single-element-bundle representations. However, when the prediction of joint kinematics is of main interest, spring ligament models provide a faster option with acceptable outcome.

A class of rate-independent lower-order gradient plasticity theories : Implementation and application to disc torsion problem

As the characteristic scale of products and production processes decreases, the plasticity phenomena observed start to deviate from those evidenced at the macroscale. The current research aims at investigating this gap using a lower-order gradient enhanced approach both using phenomenological continuum level as well as crystal plasticity models. In the phenomenological approach, a physically based hardening model relates the flow stress to the density of dislocations where it is assumed that the sources of immobile dislocations are both statistically stored (SSDs) as well as geometrically necessary dislocations (GNDs). In the crystal plasticity model, the evolution of the critical resolved shear stress is also defined based on the total number of dislocations. The GNDs are similarly incorporated in the hardening based on projecting the plastic strain gradients through the Burgers tensor on slip systems. A rate-independent formulation is considered that eliminates any artificial inhomogeneous hardening behavior due to numerical stabilization. The behavior of both models is compared in simulations focusing on the effect of structurally imposed gradients versus the inherent gradients arising in crystal plasticity simulations.

An insight in friction and wear mechanisms during hot stamping

Hot stamping is often used in the automotive industry to combine formability and strength. However, during forming process at high temperatures, friction and tool wear are determining factors that can affect the efficiency of the whole process. The goal of this paper is to investigate the effects of temperature on the local coefficient of friction and tool wear and to provide an insight in the phenomena which take place at the tool-sheet metal interface during hot stamping processes. For this purpose, hot friction draw tests between uncoated tool steel and Al-Si coated press hardening steel were carried out at several temperatures between 500-700°C. Consecutive tests were performed to mimic industrial hot stamping process and to investigate the effect of tool wear on the friction phenomenon. Finally, tool-sheet metal tribological behavior and the interaction between the friction and tool wear mechanisms were analyzed using different imaging and chemical characterization techniques. The results show that several stages can be distinguished at the interface between tool and sheet metal coating during hot stamping: flattening due to initial normal contact, ploughing of tool asperities through coating, secondary ploughing in the coating by adhered material on the tooling, and abrasive wear in the tool by embedded particles in the sheet metal coating. Furthermore, tool wear shows some major differences in the temperature range of 500-700°C. At high temperature a larger abrasive area and more severe compaction galling occurs that can be explained by material properties of Al-Si coating at elevated temperatures. The results of this study can be used for more efficient process design and a more realistic modelling of the hot stamping process.

Multi-scale contact modeling of coated steels for sheet metal forming applications

Friction in sheet metal forming is a local phenomenon which depends on continuously evolving contact conditions during the forming process. This is mainly influenced by local contact pressure, surface textures of the sheet metal as well as the forming tool surface profile and material behavior. The first step for an accurate prediction of friction is to reliably estimate real area of contact at various normal loads. In this study, a multi-scale contact model for the normal load is presented to predict asperity deformation in coated steels and thus to estimate the real area of contact. Surface profiles of the zinc layer and steel substrate are modelled explicitly obtained from confocal measurements. Different mechanical properties are assigned to the zinc coating and the steel substrate. The model was calibrated and validated relative to lab-scale normal load tests using different samples of zinc coated steel with distinct surface textures. The results show that the model is able to predict the real area of contact in zinc-coated steels for various contact pressures and different surface textures. Current multi-scale model can be used to determine the local friction coefficient in sheet metal forming processes more accurately.

The evolution of mechanical properties of AISI 301 as a result of phase reversion heat treatment, experiment and modeling

Laser heat treatments of metastable austenitic stainless steel AISI 301 are presented aiming to elucidate the relation between heat treatment, transformation and mechanical properties after heat treatment. It is assumed that the observed phase reversion of martensite to austenite is due to a diffusional transformation mechanism governed by nucleation and growth leading to submicron grains. Based on this assumption it is demonstrated that the reverse transformation can be successfully predicted by the proposed model. Subsequently the effect of the heat treatment on the hardness is reviewed. It is shown that the proposed hardness-model, in combination with the proposed isothermal transformation model, is in agreement with the observed behavior. Amongst others it is successfully predicted that the isothermal transformation precedes the recrystallization of the retained austenite and that the post-heat treatment grain size has a large effect on the behavior through the Hall-Petch effect.