Jörn Ihlemann

Analysis of some basic approaches to finite strain elasto-plasticity in view of reference change

Abstract There is a large variety of concepts used to generalize the classical Prandtl–Reuss relations of infinitesimal elasto-plasticity to finite strains. In this work, some basic approaches are compared in a qualitative way with respect to a certain invariance property. These basic approaches include the additive hypoelasto-plasticity with corotational stress rates, additive plasticity in the logarithmic strain space, and multiplicative hyperelasto-plasticity. The notion of weak invariance is introduced in this study. Roughly speaking, a material model is weakly invariant under a certain transformation of the local reference configuration if this reference change can be neutralized by a suitable transformation of initial conditions, leaving the remaining constitutive relations intact. We analyse the basic models in order to find out if they are weakly invariant under arbitrary volume-preserving transformations of the reference configuration. It is shown that the weak invariance property corresponds to a generalized symmetry which provides insights into underlying constitutive assumptions. This property can be used for a systematic study of different frameworks of finite strain elasto-plasticity. In particular, it can be used as a classification criterion.

A viscoplasticity model with an enhanced control of the yield surface distortion

Abstract A new model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is presented. The basic modeling assumptions are illustrated using a new two-dimensional rheological analogy. This demonstrative rheological model is used as a guideline for the construction of constitutive relations. The nonlinear kinematic hardening is captured using the well-known Armstrong–Frederick approach. The distortion of the yield surface is described with the help of a so-called distortional backstress. A distinctive feature of the model is that any smooth convex saturated form of the yield surface which is symmetric with respect to the loading direction can be captured. In particular, an arbitrary sharpening of the saturated yield locus in the loading direction combined with a flattening on the opposite side can be covered. Moreover, the yield locus evolves smoothly and its convexity is guaranteed at each hardening stage. A strict proof of the thermodynamic consistency is provided. Finally, the predictive capabilities of the material model are illustrated using the experimental data for a very high work hardening annealed aluminum alloy 1100 Al.

An explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity

Abstract We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean hyperelastic relations between stresses and elastic strains. The evolution equation is six dimensional and describes an incompressible flow such that the volume changes are purely elastic. For the corresponding local initial value problem, a fully implicit integration procedure is considered, and a simple explicit update formula is derived. Thus, no local iterative procedure is required, which makes the numerical scheme more robust and efficient. The resulting integration algorithm is unconditionally stable and first order accurate. The incompressibility constraint of the inelastic flow is exactly preserved. A rigorous proof of the symmetry of the consistent tangent operator is provided. Moreover, some properties of the numerical solution, like invariance under the change of the reference configuration and positive energy dissipation within a time step, are discussed. Numerical tests show that, in terms of accuracy, the proposed integration algorithm is equivalent to the classical implicit scheme based on the exponential mapping. Finally, in order to check the stability of the algorithm numerically, a representative initial boundary value problem involving finite viscoelastic deformations is considered. A FEM solution of the representative problem using MSC.MARC is presented.

Modelling and simulation of adhesive curing processes in bonded piezo metal composites

This work deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites (PMC) which consist of an adhesive layer, an integrated piezoelectric module and two surrounding metal sheet layers. In a first step, a finite strain modelling framework for the representation of polymer curing phenomena is proposed. Based on this formulation, a concretised model is deduced and applied to one specific epoxy based adhesive. Here, appropriate material functions are provided and the thermodynamic consistency is proved. Regarding the finite element implementation, a numerical scheme for time integration and a new approach for maintaining a constant initial volume at arbitrary initial conditions are provided. Finally, finite element simulations of a newly proposed manufacturing process for the production of bonded PMC structures are conducted. Thereby, a representative deep drawing process is analysed with respect to the impact of the adhesive layer on the embedded piezoelectric module.

Modelling and simulation of acrylic bone cement injection and curing within the framework of vertebroplasty

The minimal invasive procedure of vertebroplasty is a surgical technique to treat compression fractures of vertebral bodies. During the treatment, liquid bone cement gets injected into the affected vertebral body and therein cures to a solid. In order to investigate the treatment and the impact of injected bone cement, an integrated modelling and simulation framework has been developed. The framework includes (i) the generation of microstructural computer models based on microCT images of human cancellous bone, (ii) computational fluid dynamics (CFD) simulations of bone cement injection into the trabecular structure and (iii) non-linear finite element (FE) simulations of the subsequent bone cement curing. A detailed description of the material behaviour of acrylic bone cements is provided for both simulation stages. A non-linear process-dependent viscosity function is chosen to represent the bone cement behaviour during injection. The bone cements phase change from a highly viscous fluid to a solid is described by a non-linear viscoelastic material model with curing dependent properties. To take into account the distinctive temperature dependence of acrylic bone cements, both material models are formulated in a thermo-mechanically coupled manner. Moreover, the corresponding microstructural CFD- and FE-simulations are performed using thermo-mechanically coupled solvers. An application of the presented modelling and simulation framework to a sample of human cancellous bone demonstrates the capabilities of the presented approach.

Ductile damage model for metal forming simulations including refined description of void nucleation

Abstract We address the prediction of ductile damage and material anisotropy accumulated during plastic deformation of metals. A new model of phenomenological metal plasticity is proposed which is suitable for applications involving large deformations of workpiece material. The model takes combined nonlinear isotropic/kinematic hardening, strain-driven damage and rate-dependence of the stress response into account. Within this model, the work hardening and the damage evolution are fully coupled. The description of the kinematics is based on the double multiplicative decomposition of the deformation gradient proposed by Lion. An additional multiplicative decomposition is introduced in order to account for the damage-induced volume increase of the material. The model is formulated in a thermodynamically admissible manner. Within a simple example of the proposed framework, the material porosity is adopted as a rough measure of damage. A new simple void nucleation rule is formulated based on the consideration of various nucleation mechanisms. In particular, this rule is suitable for materials which exhibit a higher void nucleation rate under torsion than in case of tension. The material model is implemented into the FEM code Abaqus and a simulation of a deep drawing process is presented. The robustness of the algorithm and the performance of the formulation is demonstrated.

Experimental—numerical investigation of the rolling process of high gears

Rolling of high gears into full material is a new and economic way of manufacturing. Such gearings provide a higher surface strength and a better surface quality than conventional gearings. However, higher expenses for tools are disadvantageous. So far, the design of the forming tools follows only geometric requirements and the loads at the tool surface are not considered for designing these tools. To increase the life cycle of the tools, the loads at the tool surface and the stress state at the contact zone have to be taken into account. This paper presents an experimental setup to record strain data at the forming tool during the processing. Results of these measurements are shown for several stages of the process. Numerical simulations, according to the experimental tests, are shown in the second part. A staggered simulation with a two-dimensional model of the forming process is used to identify contact loads at the tool surface. These loads are transferred to a three-dimensional numerical model of the forming tool and the procedure to transfer loads is described in this article. The validation of the numerical results with the measured strain data shows the applicability of the numerical approach for designing tools.

On the development of an intrinsic hybrid composite

Hybrid parts, which combine low weight with high strength, are moving into the focus of the automotive industry, due to their high potential for usage in the field of crash-relevant structures. In this contribution, the development of an intrinsic hybrid composite is presented, with a focus on the manufacturing process, complex simulations of the material behaviour and material testing. The hybrid composite is made up of a continuous fibre- reinforced plastic (FRP), in which a metallic insert is integrated. The mechanical behaviour of the individual components is characterised. For material modelling, an approach is pointed out that enables modelling at large strains by directly connected rheological elements. The connection between the FRP and the metallic insert is realised by a combination of form fit and adhesive bonds. On the one hand, adhesive bonds are generated within a sol gel process. On the other hand, local form elements of the metallic insert are pressed into the FRP. We show how these form elements are generated during the macroscopic forming process. In addition, the applied sol gel process is explained. Finally, we consider design concepts for a specimen type for high strain testing of the resulting interfaces.

Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.

FE-simulation of the Presta joining process for assembled camshafts - local widening of shafts through rolling

Considerable weight benefits and the option to combine various steel alloys of the single parts are the major advantages of assembled over conventional camshafts. The Presta joining process is the leading manufacturing method of assembled camshafts in the global market. The process is divided into two substeps. At first, the outer diameter of the shaft is widened with a profile oriented orthogonal to the shaft axis at the intended cam seat. At this position the shaft is subsequently joined with a cam with an internal profile oriented parallel to the shaft axis. As a result, these perpendicular profiles form a tight fit due to plastic deformations. Consequently the simulation of the manufacturing process has to start with the simulation of the rolling of the shaft. The resulting profile requested in this step is axisymmetric, but the arrangement of tools is not. Thus a three-dimensional model is required, which is presented in this work. Furthermore, the infeed of the rolling tool is unknown and controlled by the stiffness of the holders of the rolling tool. This work shows the modeling of this behavior. To predict realistic results for the underlying process, the use of precise material models is essential in order to take several hardening mechanisms into account. However, the use of complex material models implies additional effort, which is shown in this work.