Emin Semih Perdahcioglu

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.

Gradient Enhanced Physically Based Plasticity: Implementation and Application to a Problem Pertaining Size Effect

A physically based plasticity model is implemented which describes work hardening of a material as a function of the total dislocation density. The local part of the model, which involves statistically stored dislocations (SSDs) only, is based on Bergstrom’s original model. The nonlocal part is based on geometrically necessary dislocations (GNDs) which appear and evolve due to existence of large plastic strain gradients. The evolution of GNDs with respect to strain gradients is described based on the flow theory. The gradients are computed explicitly using the converged plastic strain field and the coupling is achieved using a staggered (weak) approach. Gradient computation is carried out using an effcient algorithm that makes use of plastic strain increments at integration points whose arrangement is not necessarily regular. The algorithm is applied on a void growth problem in which high strain gradients occur around the void due to stress concentrations.

Gradient Enhanced Physically Based Plasticity: Implementation and Application to a Problem Pertaining Size Effect : Implementation and application to a problem pertaining size effect

A physically based plasticity model is implemented which describes work hardening of a material as a function of the total dislocation density. The local part of the model, which involves statistically stored dislocations (SSDs) only, is based on Bergstroms original model. The nonlocal part is based on geometrically necessary dislocations (GNDs) which appear and evolve due to existence of large plastic strain gradients. The evolution of GNDs with respect to strain gradients is described based on the flow theory. The gradients are computed explicitly using the converged plastic strain field and the coupling is achieved using a staggered (weak) approach. Gradient computation is carried out using an effcient algorithm that makes use of plastic strain increments at integration points whose arrangement is not necessarily regular. The algorithm is applied on a void growth problem in which high strain gradients occur around the void due to stress concentrations.

Implementation and application of a gradient enhanced crystal plasticity model

A rate-independent crystal plasticity model is implemented in which description of the hardening of the material is given as a function of the total dislocation density. The evolution of statistically stored dislocations (SSDs) is described using a saturating type evolution law. The evolution of geometrically necessary dislocations (GNDs) on the other hand is described using the gradient of the plastic strain tensor in a non-local manner. The gradient of the incremental plastic strain tensor is computed explicitly during an implicit FE simulation after each converged step. Using the plastic strain tensor stored as state variables at each integration point and an efficient numerical algorithm to find the gradients, the GND density is obtained. This results in a weak coupling of the equilibrium solution and the gradient enhancement. The algorithm is applied to an academic test problem which considers growth of a cylindrical void in a single crystal matrix.

Constitutive modeling of hot horming of austenitic stainless steel 316LN by accounting for recrystallization in the dislocation evolution

Hot compression test data taken from Zhang [1] of metastable austenitic stainless steel AISI 316LN over a range of strain rates and temperatures shows typical dynamic recovery and recrystallization behavior. It is proposed to model this behavior by incorporating not only the hardening and recovery into the Bergstrom dislocation evolution equation, but also the recrystallization. It is shown that the initial mechanical response before recrystallization can be accurately represented by assuming that the mean free path evolves as the microstructure evolves from homogeneously spaced dislocations to cell-pattern. Results show that this novel continuum mechanical model can predict the observed behavior, showing a good match to the experimental data and capturing the transition from recrystallization to (almost) no recrystallization.

Modeling of the Austenite-Martensite Transformation in Stainless and TRIP Steels

The transformation of austenite to martensite is a dominant factor in the description of the constitutive behavior during forming of TRIP assisted steels. To predict this transformation different models are currently available. In this paper the transformation is regarded as a stress induced process based on the thermodynamic action of the local stresses during transformation. A threshold for the thermodynamic action, above which transformation will occur, can be easily measured in a properly instrumented tensile test. The martensitic transformation is a diffusionless lattice shear. It is characterized by a habit plane normal n and a shear vector m, which are both defined with respect to the austenite lattice coordinate system. Therefore the thermodynamic action in each material grain strongly depends on the orientation of the grain with respect to the applied stress. Uniaxial tensile tests on both a non-textured austenitic stainless steel and one with a strong crystallographic texture were performed in both the rolling and the transverse directions. Both materials show mechanically induced phase transformation from austenite to martensite. When a strong texture is present in the austenite, differences between transformations during deformation in different directions can be observed clearly. The stress induced transformation theory, in combination with the textures measured before and after deformation, is used to explain and model the difference in transformation behavior when straining in various directions. During deformation the texture changes. This can have consequences for modeling of the transformation during non-proportional deformation.

A model for TRIP steel constitutive behaviour

A constitutive model is developed for TRIP steel. This is a steel which contains three or four different phases in its microstructure. One of the phases in TRIP steels is metastable austenite (Retained Austenite) which transforms to martensite upon deformation. The accompanying transformation strain and the increase in hardness provide excellent formability characteristics. The phase transformation depends on the stress in the austenite, which is not equal to the overall stress. An estimate of the local stress in the austenite is obtained by homogenization of the response of the phases using a Mean-Field homogenization method. Overall stress strain results as well as stress strain results for individual phases are compared to measurements found in literature. The model can be used in finite element simulations of forming processes.

A constitutive model for multi‐phase steels

Mean‐Field homogenization algorithms for materials involving two or more elastic‐plastic constituent phases are investigated. The Voigt, Reuss and Self consistent schemes which are directly applicable to multi‐phase systems are implemented. The shortcomings of these schemes are accuracy for the former two and computational efficiency for the latter. A new interpolative model is proposed which is aimed to be both computationally efficient and accurate. The results of the models are studied on the material point level for a prescribed uniaxial tensile deformation. It is observed that the response computed by the proposed scheme closely matches that computed by the Self Consistent approach.

A continuum model for the effect of dynamic recrystallization on the stress-strain response

Austenitic Stainless Steels and High-Strength Low-Alloy (HSLA) steels show significant dynamic recovery and dynamic recrystallization (DRX) during hot forming. In order to design optimal and safe hot-formed products, a good understanding and constitutive description of the material behavior is vital. A new continuum model is presented and validated on a wide range of deformation conditions including high strain rate deformation. The model is presented in rate form to allow for the prediction of material behavior in transient process conditions. The proposed model is capable of accurately describing the stress–strain behavior of AISI 316LN in hot forming conditions, also the high strain rate DRX-induced softening observed during hot torsion of HSLA is accurately predicted. It is shown that the increase in recrystallization rate at high strain rates observed in experiments can be captured by including the elastic energy due to the dynamic stress in the driving pressure for recrystallization. Furthermore, the predicted resulting grain sizes follow the power-law dependence with steady state stress that is often reported in literature and the evolution during hot deformation shows the expected trend.

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.