Simulation of Rate Dependent Plasticity of Polymers

Polycarbonate is an amorphous polymer which exhibits nonlinear deformation before failure. It shows a pronounced strength-differential effect between compression and tension. Strain rate influences the mechanical response of the polycarbonate. In particular, the yield stress is increased with increasing strain rate. The concept of stress mode dependent weighting function is used in the proposed model to simulate the asymmetric effects for different loading speeds. In this concept, an additive decomposition of the flow rule is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The resulting evolution equations are updated using a backward Euler scheme and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation of the resulting set of constitutive equations is used in a finite element program for parameter identification. The proposed model is verified by showing a good agreement with the experimental data. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vortex wake mitigation of an airfoil with winglets by active rudders

The wake vortex hazard and the required separation distances between aircraft at airports constitute an impediment to the growth of air traffic at major hubs. One approach to reduce separation distances is the exploitation of the inherent instability in vortex systems, leading to an accelerated breakdown. In this paper we show the impact of excitation by different control surfaces on the stability behavior of the wake of a rectangular wing with winglets. The experiment shows that the excitation through winglet rudders and ailerons yields the best results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient parallel simulation of biphasic materials in biomechanics

Biphasic materials are widely used for the modelling and the numerical simulation of articular cartilage within joints. In combination with contact, the numerical solution of the arising discrete systems is a demanding task, in particular for realistic geometries. We consider the stability and efficiency of different multilevel approaches for the numerical solution of the resulting non–smooth systems. Moreover, multilevel methods are derived which allow for the efficient numerical simulation of biphasic materials in contact. Numerical examples on problem specific geometries in three space dimensions are given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A thermodynamic framework for coupled multiphase field and diffusion models for lower bainite transformation

The lower bainite transformation is characterized by a displacive transformation from austenite to bainitic ferrite and a subsequent separation of carbon within the new supersaturated phase. At accumulations of carbon carbides precipitate. To model this complex process a framework considering phase changes and carbon diffusion is required. In this work we present a thermodynamic framework based on the theory of microforce balances considering multiphase Ginzburg-Landau equations coupled with Cahn-Hilliard diffusion. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two accuracy improvements on nonuniform transformation field analysis for plasticity coupled to softening

A reduced order homogenization scheme for the case of plasticity coupled with softening effects is proposed. This is based on a straightforward extension of the so-called nonuniform transformation field analysis (NTFA, [2]). Two related new methods, denoted as uneven NTFA and adaptive NTFA accounting for accuracy improvements, are also presented, which are based on the ideas of parameter identification and adaptive modeling, respectively. A complementary numerical study is given. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A macroscopic consitutive model on induced anisotropy for polymers with weighting functions

The alignment of polymer chains is a well known microstructural evolution effect due to straining of polymers. This has a drastic influence on the macroscopic properties of the initially isotropic material, such as a pronounced strength in the loading direction of stretched films. Experiments on strain induced anisotropy at room temperature are analyzed by optical measurements. For modeling the effect of strain induced anisotropy a macroscopic constitutive model is presented. As a key idea, weighting functions are introduced to represent a strain-softening/hardening-effect to account for induced anisotropy. These functions represent the ratio between the total strain rate and a structural tensor. In this way, material parameters are used as a sum of weighted direction related quantities. In the finite element examples we simulate the cold-forming of amorphous thermoplastic films below the glass transition temperature subjected to different re-loading directions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macroscopic and mesoscopic modeling based on the concept of generalized stresses for cutting simulation

Based on the concept of generalized stresses proposed by GURTIN [2] and FOREST et al. [1] macro- and meso-scopic modelling are presented. For the macroscopic modelling we develop a multi-mechanism model for strain rate and temperature dependent asymmetric plastic material behavior accompanied by phase transformation with consideration of the trip-strain. Furthermore, we extend the multi-mechanism model with the gradient of phase fraction, which is considered as an extra degree of freedom. For mesoscopic modelling a phase field model is implemented for describing phase transformations. For the scenario of a cutting process we have a martensite-austenite-martensite transformation. A generalized principle of virtual power is postulated involving generalized stresses and used to derive the constitutive equations for both approaches. Furthermore, parameters of the multi-mechanism model related to visco-plasticity with SD-effect and the trip-strain are identified for the material DIN 100Cr6. In the examples a cutting simulation for testing the multi-mechanism model and a phase-transformation simulation are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical homogenisation – application to HVOF thermal-sprayed WC-Co coatings

Hard material coatings are widely employed as wear protection for highly engrossed surfaces. For example, coatings consisting of tungsten carbide (WC) and cobalt (Co) are used for sheet metal forming tools. A relatively cost-efficient coating technique is the high velocity oxygen fuel (HVOF) thermal spraying process which, as a trade-off, induces a large amount of energy into the heterogeneous coating and the substrate. Hence, this leads to a complex transient, thermomechanically coupled problem. In order to predict the residual stresses during the quenching procedure, a two scale finite element framework is established wherein the scale bridging is performed by application of two different homogenisation approaches. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local Tensor Valuations

The local Minkowski tensors are valuations on the space of convex bodies in Euclidean space with values in a space of tensor measures. They generalize at the same time the intrinsic volumes, the curvature measures and the isometry covariant Minkowski tensors that were introduced by McMullen and characterized by Alesker. In analogy to the characterization theorems of Hadwiger and Alesker, we give here a complete classification of all locally defined tensor measures on convex bodies that share with the local Minkowski tensors the basic geometric properties of isometry covariance and weak continuity.